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When the electron beam strikes the fluorescent screen, it gives off light at that spot. Horizontal deflection plates Bright spot on fluorescent screen Electron trajectory Figure 1.

The first one deals with the TV picture tube and the other with how electric utilities determine your electric bill. This then became the basis for the picture tube used for so many years for televisions. It is still the most economical device today, although the price of flat-screen systems is rapidly becoming competitive.

Before the Braun tube could be used in television, it took the inventiveness of Vladimir K. Zworykin — to develop the iconoscope so that the modern television would become a reality. The iconoscope developed into the orthicon and the image orthicon, which allowed images to be captured and converted into signals that could be sent to the television receiver.

Thus, the television camera was born. The electron beam in a TV picture tube carries electrons per second. As a design engineer, determine the voltage Vo needed to accelerate the electron beam to achieve 4 W.

Solution: The charge on an electron is e 1. The beam power is p Voi or Vo p 4 25, V i 1. Practice Problem 1. Answer: 48 mW. The cost of electricity depends upon the amount of energy consumed in kilowatt-hours kWh.

Other factors that affect the cost include demand and power factors; we will ignore these for now. However, even if a consumer uses no energy at all, there is a minimum service charge the customer must pay because it costs money to stay connected to the power line.

As energy consumption increases, the cost per kWh drops. It is interesting to note the average monthly consumption of household appliances for a family of five, shown in Table 1. A homeowner consumes kWh in January. Determine the electricity bill for the month using the following residential rate schedule: Example 1. Solution: We calculate the electricity bill as follows. Carefully define the problem.

Establish a set of alternative solutions and determine the one that promises the greatest likelihood of success. Has the problem been solved satisfactorily? Time spent at this point clearly identifying the problem will save you considerable time and frustration later.

A problem presented to you in industry may require that you consult several individuals. At this step, it is important to develop questions that need to be addressed before continuing the solution process.

If you have such questions, you need to consult with the appropriate individuals or resources to obtain the answers to those questions.

With those answers, you can now refine the problem, and use that refinement as the problem statement for the rest of the solution process. You are now ready to write down everything you know about the problem and its possible solutions. This important step will save you time and frustration later. Almost every problem will have a number of possible paths that can lead to a solution. It is highly desirable to identify as many of those paths as possible.

At this point, you also need to determine what tools are available to you, such as PSpice and MATLAB and other software packages that can greatly reduce effort and increase accuracy. Again, we want to stress that time spent carefully defining the problem and investigating alternative approaches to its solution will pay big dividends later.

Evaluating the alternatives and determining which promises the greatest likelihood of success may be difficult but will be well worth the effort. Document this process well since you will want to come back to it if the first approach does not work. The process you follow must be well documented www. This detailed evaluation may lead to corrections that can then lead to a successful solution.

It can also lead to new alternatives to try. Many times, it is wise to fully set up a solution before putting numbers into equations. This will help in checking your results. You now thoroughly evaluate what you have accomplished. Decide if you have an acceptable solution, one that you want to present to your team, boss, or professor. Now you need to present your solution or try another alternative. At this point, presenting your solution may bring closure to the process.

Often, however, presentation of a solution leads to further refinement of the problem definition, and the process continues. Following this process will eventually lead to a satisfactory conclusion. Now let us look at this process for a student taking an electrical and computer engineering foundations course.

The basic process also applies to almost every engineering course. Keep in mind that although the steps have been simplified to apply to academic types of problems, the process as stated always needs to be followed.

We consider a simple example. To solve for i8 using circuit analysis will eventually lead to a solution, but it will likely take more work than either nodal or mesh www.

To solve for i8 using mesh analysis will require writing two simultaneous equations to find the two loop currents indicated in Fig. Therefore, we will solve for i8 using nodal analysis. We first write down all of the equations we will need in order to find i8.

Applying KVL to loop 2, v8 v4 3 i2 8 i3 4 3 0. The current through the 8- resistor is 0. Answers: 1. Problems Section 1. Calculate how much charge passes through any cross-section of the conductor in 20 s. Sketch the corresponding current. The current flowing past a point in a device is shown in Fig.

Calculate the total charge through the point. For Prob. The current through an element is shown in Fig. Determine the total charge that passed through the element at: a t 1 s b t 3 s c t 5 s b Calculate the power absorbed. Section 1. Sections 1. How much charge is deposited on the object? How much charge can it release at that rate? If its terminal voltage is 1. If p1 W, p2 60 W, p4 45 W, p5 30 W, calculate the power p3 received or delivered by element 3.

How many coulombs of charge are deposited on the plane? How many electrons and coulombs flow through the bulb in one day? If a consumer operates a W light bulb continuously for one day, how much is the consumer charged? Find the cost of operating the toaster once per day for 1 month 30 days.

Calculate: b Figure 1. Determine: Figure 1. If a customer uses 1, kWh in one month, how much will Reliant Energy charge? Comprehensive Problems 1. How many coulombs of charge were contained in the lightning bolt? Calculate: 8. A lead-acid battery is rated at Ah. Calculate the total energy in MWh consumed by the plant. A small electric car is equipped with a hp electric motor.

How much energy does the motor deliver in one hour, assuming the motor is operating at maximum power for the whole time? Assume that 1 horsepower W. How long does it take for a charge of 15 C to pass through the wire? Engineers must be able to design and conduct experiments, as well as analyze and interpret data.

Most students have spent many hours performing experiments in high school and in college. During this time, you have been asked to analyze the data and to interpret the data. Therefore, you should already be skilled in these two activities. My recommendation is that, in the process of performing experiments in the future, you spend more time in analyzing and interpreting the data in the context of the experiment. What does this mean?

If you are looking at a plot of voltage versus resistance or current versus resistance or power versus resistance, what do you actually see? Does the curve make sense? Does it agree with what the theory tells you? Does it differ from expectation, and, if so, why?

Clearly, practice with analyzing and interpreting data will enhance this skill. Since most, if not all, the experiments you are required to do as a student involve little or no practice in designing the experiment, how can you develop and enhance this skill?

Actually, developing this skill under this constraint is not as difficult as it seems. What you need to do is to take the experiment and analyze it. Just break it down into its simplest parts, reconstruct it trying to understand why each element is there, and finally, determine what the author of the experiment is trying to teach you. Even though it may not always seem so, every experiment you do was designed by someone who was sincerely motivated to teach you something.

To actually determine the values of these variables in a given circuit requires that we understand some fundamental laws that govern electric circuits. In this chapter, in addition to these laws, we shall discuss some techniques commonly applied in circuit design and analysis.

These techniques include combining resistors in series or parallel, voltage division, current division, and delta-to-wye and wye-to-delta transformations. The application of these laws and techniques will be restricted to resistive circuits in this chapter. We will finally apply the laws and techniques to real-life problems of electrical lighting and the design of dc meters. This physical property, or ability to resist current, is known as resistance and is represented by the symbol R.

Good conductors, such as copper and aluminum, have low resistivities, while insulators, such as mica and paper, have high resistivities. Table 2. The circuit element used to model the current-resisting behavior of a material is the resistor.

For the purpose of constructing circuits, resistors are usually made from metallic alloys and carbon compounds. The resistor is the simplest passive element. Georg Simon Ohm —a German physicist, is credited with finding the relationship between current and voltage for a resistor. That is, v r i Ohm defined the constant of proportionality for a resistor to be the resistance, R.

The resistance is a material property which can change if the internal or external conditions of the element are altered, e. Thus, Eq. R in Eq. Thus, The resistance R of an element denotes its ability to resist the flow of electric current; it is measured in ohms. We may deduce from Eq. The direction of current i and the polarity of voltage v must conform with the passive Historical Georg Simon Ohm —a German physicist, in experimentally determined the most basic law relating voltage and current for a resistor.

Born of humble beginnings in Erlangen, Bavaria, Ohm threw himself into electrical research. His efforts resulted in his famous law. Inhe was given the Professor of Physics chair by the University of Munich. To honor him, the unit of resistance was named the ohm. This implies that current flows from a higher potential to a lower potential in order for v i R.

If current flows from a lower potential to a higher potential, v i R. Since the value of R can range from zero to infinity, it is important that we consider the two extreme possible values of R.

An element with R 0 is called a short circuit, as shown in Fig. In practice, a short circuit is usually a connecting wire assumed to be a perfect conductor. Thus, A short circuit is a circuit element with resistance approaching zero. Similarly, an element with R is known as an open circuit, as shown in Fig. For an open circuit, i lim b RS Figure 2. Thus, An open circuit is a circuit element with resistance approaching infinity. A resistor is either fixed or variable. Most resistors are of the fixed type, meaning their resistance remains constant.

The two common types of fixed resistors wirewound and composition are shown in Fig. The composition resistors are used when large resistance is needed. The circuit symbol in Fig. Variable resistors have adjustable resistance. The symbol for a variable resistor is shown in Fig.

A common variable resistor is known as a potentiometer or pot for short, with the symbol shown in Fig. The pot is a three-terminal element with a sliding contact or wiper.

By sliding the wiper, the resistances between the wiper terminal and the fixed terminals vary. Like fixed resistors, variable resistors can be of either wirewound or composition type, as shown in Fig. Although resistors like those in Figs. Courtesy of Tech America. Variable resistors: a composition type, b slider pot.

It has a constant resistance and thus its current-voltage characteristic is as illustrated in Fig. Its resistance varies with current and its i-v characteristic is typically shown in Fig.

Examples of devices with nonlinear resistance are the lightbulb and the diode. Although all practical resistors may exhibit nonlinear behavior under certain conditions, we will assume in this book that all elements actually designated as resistors are linear. A useful quantity in circuit analysis is the reciprocal of resistance R, known as conductance and denoted by G: 33 Figure 2.

The unit of conductance is the mho ohm spelled backward or reciprocal ohm, with symbolthe inverted omega. For example, 10 is the same as 0. Using Eqs. The power dissipated in a resistor is a nonlinear function of either current or voltage. Since R and G are positive quantities, the power dissipated in a resistor is always positive. Thus, a resistor always absorbs power from the circuit. This confirms the idea that a resistor is a passive element, incapable of generating energy. Find its resistance.

How much current is drawn by a toaster with resistance 10 at V? Example 2. Figure 2. Find the current through the resistor and the power dissipated. To differentiate between a circuit and a network, we may regard a network as an interconnection of elements or devices, whereas a circuit is a network providing one or more closed paths. The convention, when addressing network topology, is to use the word network rather than circuit.

We do this even though the words network and circuit mean the same thing when used in this context. In network topology, we study the properties relating to the placement of elements in the network and the geometric configuration of the network.

Such elements include branches, nodes, and loops. A branch represents a single element such as a voltage source or a resistor. The circuit in Fig. A node is the point of connection between two or more branches. If a short circuit a connecting wire connects two nodes, the two nodes constitute a single node. Notice that the three points that form node b are connected by perfectly conducting wires and therefore constitute a single point.

The same is true of the four points forming node c. We demonstrate that the circuit in Fig. The two circuits in Figs. However, for the sake of clarity, nodes b and c are spread out with perfect conductors as in Fig. Find i and R. A loop is said to be independent if it contains at least one branch which is not a part of any other independent loop. Independent loops or paths result in independent sets of equations.

It is possible to form an independent set of loops where one of the loops does not contain such a branch. A second loop with the 3 resistor and the current source is independent. The third loop could be the one with the 2 resistor in parallel with the 3 resistor. This does form an independent set of loops. A network with b branches, n nodes, and l independent loops will satisfy the fundamental theorem of network topology: bln1 2.

Two or more elements are in series if they exclusively share a single node and consequently carry the same current. Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them. Elements are in series when they are chain-connected or connected sequentially, end to end.

For example, two elements are in series if they share one common node and no other element is connected to that common node. Elements in parallel are connected to the same pair of terminals. Elements may be connected in a way that they are neither in series nor in parallel. In the circuit shown in Fig. The 2- resistor, the 3- resistor, and the current source are in parallel because they are connected to the same two nodes b and c and consequently have the same voltage across them.

The 5- and 2- resistors are neither in series nor in parallel with each other. Identify which elements are in series and which are in parallel. Solution: Since there are four elements in the circuit, the circuit has four branches: 10 V, 56and 2 A.

The circuit has three nodes as identified in Fig. The 5- resistor is in series with the V voltage source because the same current would flow in both. The 6- resistor is in parallel with the 2-A current source because both are connected to the same nodes 2 and 3. Answer: Five branches and three nodes are identified in Fig. The 1- and 2- resistors are in parallel. The 4- resistor and V source are also in parallel.

Answer for Practice Prob. Mathematically, KCL implies that N a in 0 2. By this law, currents www. Identify the elements that are in series and in parallel. To prove KCL, assume a set of currents ik tk 1, 2, pflow into a node. The Teacher (feat. Cabes MC) - D-Solution sum of currents at the node is iT t i1 t i2 t i3 t p i1 Integrating both sides of Eq.

But the law of conservation of electric charge requires that the algebraic sum of electric charges at the node must not change; that is, the node stores no net charge. Consider the node in Fig. Applying KCL gives Cabes MC - Teacher EP (All Media) i2 i3 i4 i5 0 Closed boundary 2.

By rearranging the terms, we get i1 i3 i4 i2 i5 2. Two sources or circuits in general are said to be equivalent if they have the same i-v relationship at a pair of terminals.

Note that KCL also applies to a closed boundary. This may be regarded as a generalized case, because a node may be regarded as a closed surface shrunk to a point. In two dimensions, a closed boundary is the same as a closed path. As typically illustrated in the circuit of Fig. A simple application of KCL is combining current sources in parallel. The combined current is the algebraic sum of the current supplied by the individual sources. For example, the current sources shown in www. Born the son of a lawyer in Konigsberg, East Prussia, Kirchhoff entered the University of Konigsberg at age 18 and later became a lecturer in Berlin.

His collaborative work in spectroscopy with German chemist Robert Bunsen led to the discovery of cesium in and rubidium in Kirchhoff was also credited with the Kirchhoff law of radiation. Thus Kirchhoff is famous among engineers, chemists, and physicists.

The combined or equivalent current source can be found by applying KCL to node a. To illustrate KVL, consider the circuit in Fig. The sign on each voltage is the polarity of the terminal encountered first as we travel around the loop. We can start with any branch and go around the loop either clockwise or counterclockwise.

Suppose we start with the voltage source and go clockwise around the loop as shown; then voltages would be v1, v2, v3, v4, and v5, in that order. For example, as we reach branch 3, the positive terminal is met first; hence, we have v3. For branch 4, we reach the negative terminal first; hence, v4. Thus, KVL yields v1 v2 v3 v4 v5 0 KVL can be applied in two ways: by taking either a clockwise or a counterclockwise trip around the loop. Either way, the algebraic sum of voltages around the loop is zero.

Sum of voltage drops Sum of voltage rises 2. Notice that if we had traveled counterclockwise, the result would have been v1, v5, v4, v3, and v2, which is the same as before except that the signs are reversed. Hence, Eqs. When voltage sources are connected in series, KVL can be applied to obtain the total voltage. The combined voltage is the algebraic sum of the voltages of the individual sources.

For example, for the voltage sources shown in Fig. Vab V1 V2 V3 0 www. For the circuit in Fig. Assume that current i flows through the loop as shown in Fig. Find vx and vo in the circuit of Fig. Practice Problem 2. Find vo and io in the circuit of Fig. Answer: 8 V, 4 A. At node a, KCL gives i1 i2 i3 0 2. We express v1 and v2 in terms of i1 and i2 as in Eq. Equation 2. From the value of i2, we now use Eqs.

The process of combining the resistors is facilitated by combining two of them at a time. With this in mind, consider the single-loop circuit of Fig. The two resistors www. An equivalent circuit such as the one in Fig.

In general, The equivalent resistance of any number of resistors connected in series is the sum of the individual resistances. Resistors in series behave as a single resistor whose resistance is equal to the sum of the resistances of the individual resistors. This is called the principle of voltage division, and the circuit in Fig.

In general, if a voltage divider has N resistors R1, R2. Applying KCL at node a gives the total current i as i i1 i2 2. It must be emphasized that this applies only to two resistors in parallel. We can extend the result in Eq. Basic Laws For example, if four resistors are connected in parallel, their equivalent resistance is It is often more convenient to use conductance rather than resistance when dealing with resistors in parallel.

This means that we may replace the circuit in Fig. Notice the similarity between Eqs. The equivalent conductance of parallel resistors is obtained the same way as the equivalent resistance of series resistors. In the same manner, the equivalent conductance of resistors in series is obtained just the same way as the resistance of resistors in parallel.

Thus the equivalent conductance Geq of N resistors in series such as shown in Fig. This is known as the principle of current division, and the circuit in Fig. Notice that the larger current flows through the smaller resistance. As an extreme case, suppose one of the resistors in Fig. This means that the entire current i bypasses R1 and flows through the short circuit R2 0, the path of least resistance. Thus when a circuit www.

The equivalent resistance Req 0. The entire current flows through the short circuit. Such an equivalent resistance is the resistance between the designated terminals of the network and must exhibit the same i-v characteristics as the original network at the terminals.

Solution: To get Req, we combine resistors in series and in parallel. The 6- and 3- resistors are in parallel, so their equivalent resistance is 63 2 6 3 63 The symbol is used to indicate a parallel combination. Also, the 1- and 5- resistors are in series; hence their equivalent resistance is Thus the circuit in Fig. The current still flows through the path of least resistance, R1. By taking the limit of Eq. If we divide both the numerator and denominator by R1R2, Eq.

Solution: The 3- and 6- resistors are in parallel because they are connected to the same two nodes c and b. Their combined resistance is 36 www. This 2- equivalent resistance is now in series with the 1- resistance to give a combined resistance of 1 2 3. Thus, we replace the circuit in Fig. This 1. Find the equivalent conductance Geq for the circuit in Fig. Hence, Geq 6 4 10 S We should note that the circuit in Fig. While the resistors in Fig.

To show that the circuits are the same, we find Req for the circuit in Fig. Answer: 4 S. Calculate the power dissipated in the 3- resistor. Solution: The 6- and 3- resistors are in parallel, so their combined resistance is 63 63 2 63 Thus our circuit reduces to that shown in Fig. Notice that vo is not affected by the combination of the resistors because the resistors are in parallel and therefore have the same voltage vo.

From Fig. Another way is to apply voltage division, since the 12 V in Fig. Also calculate i1 and i2 and the power dissipated in the and resistors. For the circuit shown in Fig. Solution: a The 6-k and k resistors are in series so that their combined value is 6 12 18 k. Thus the circuit in Fig. We now apply the current division technique to find i1 and i2. This is one way of checking results. R1 R2 R3 2. R6 Wye-Delta Transformations Situations often arise in circuit analysis when the resistors are neither in parallel nor in series.

For example, consider the bridge circuit in Fig. How do we combine resistors R1 through R6 when the resistors are neither in series nor in parallel?

Many circuits of the type shown in Fig. These are www. These networks occur by themselves or as part of a larger network. They are used in three-phase networks, electrical filters, and matching networks.

Our main interest here is in how to identify them when they occur as part of a network and how to apply wye-delta transformation in the analysis of that network. Delta to Wye Conversion Suppose it is more convenient to work with a wye network in a place where the circuit contains a delta configuration. We superimpose a wye network on the existing delta network and find the equivalent resistances in the wye network.

For terminals 1 and 2 in Figs. R3 Wye to Delta Conversion c Figure 2. To obtain the conversion formulas for transforming a wye network to an equivalent delta network, we note from Eqs.

Note that in making the transformation, we do not take anything out of the circuit or put in anything new. We are merely substituting different but mathematically equivalent three-terminal network patterns to create a circuit in which resistors are either in series or in parallel, allowing us to calculate Req if necessary. Solution: Using Eqs. Answer: RaRb 70Rc The problem is clearly defined. Please note, this part normally will deservedly take much more time. Clearly, when we remove the voltage source, we end up with a purely resistive circuit.

Mains Which of the following compounds will exhibit cis-trans geometrical isomerism? Benzene reacts with CH 3 Cl in the presence of anhydrous AlCl 3 to form a chlorobenzene b benzyl chloride c xylene d toluene. Predict the product Cobtained in the following reaction of 1-butyne. Which of the compound with molecular formula C 5 H 10 yields acetone on ozonolysis? Which one of the following alkenes will react faster with H 2 under catalytic hydrogenation conditions?

Using anhydrous AlCl 3 as catalyst, which one of the following reactions produces ethylbenzene PhEt? Reaction of HBr with propene in the presence of peroxide gives a isopropyl bromide b 3-bromopropane c allyl bromide d n-propyl bromide. Which one of the following is a free-radical substitution reaction? In preparation of alkene from alcohol using Al 2 0 3 which is the effective factor?

Which reagent converts propene to 1-propanol? Which is maximum stable? When acetylene is passed through dil. H 2 S0 4 in the presence of HgS0 4the compound formed is a acetic acid b ketone c ether d acetaldehyde. Which of the following compounds will be most easily attacked by an electrophile? The major product obtained is a transpentene b 1-pentene c 2-ethoxy pentane d 2-cis-pentene.

Which of the following reaction is expected to readily give a hydrocarbon product in good yields? NaHC0 3. In the commercial gasolines, the type of hydrocarbons which are more desirable is a linear unsaturated hydrocarbon b toluene c branched hydrocarbon d straight-chain hydrocarbon. The most stable conformation of n-butane is a gauche b staggered c skew boat d eclipsed. Which of the following has zero dipole moment? Reduction of 2-butyne with sodium in liquid ammonia gives predominantly a cisbutene b no reaction c transbutene d n-butane.

A compound is treated with NaNH 2 to give sodium salt. Identify the compound. Which is the correct symbol relating the two Kekule structures of benzene?

Which is the most suitable reagent among the following to distinguish compound 3 from rest of the compounds? KMn0 4 d Ammoniacal silver nitrate. A beam of light consisting of red, green and j blue colours is incident on a right angled prism. AlPMT a not separate the three colours at all b separate the red colour part from the green and blue colours c separate the blue colour part from the red and green colours d separate all the three colours from one another.

In an astronomical telescope in normal adjustment a straight black line of length L is drawn on inside part of objective lens. The eye-piece forms a real image of this line. The length of this image is I. Aipmt The magnification of the telescope is. Two identical thin piano-convex glass lenses refractive index 1.

The intervening space is filled with oil of refractive index I. In a double slit experiment, the two slits are 1 mm apart and the screen is placed 1 m away. A monochromatic light of wavelength nm is used. What will be the width of each slit for obtaining ten maxima of double slit within the central maxima of single slit pattern?

The angle of a prism is A. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. A piano convex lens fits exactly into a piano concave lens. Their plane surfaces are parallel to each other. At what minimum distance from the common central bright fringe on the screen 2 m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?

For a normal eye, the cornea of eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D.

Using this information, the distance between the retina and the cornea-eye lens can be estimated to be NEET A parallel beam of fast moving electrons is incident normally on a narrow slit. A fluorescent screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statements is correct? The separation between the slits is reduced to half. A diffraction pattern formed on a screen placed perpendicular to the direction of the incident beam.

At the second minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of slit is Karnataka NEET When a biconvex lens of glass having refractive index 1. This implies that the liquid must have refractive index Prelims A ray of light is incident at an angle of incidence i, on one face of a prism of angle A assumed to be small and emerges normally from the opposite face.

A concave mirror of focal length f 1is placed at a distance of d from a convex lens of focal length f 2. A beam of light coming from infinity and falling on this convex lens — concave mirror combination returns to infinity. The distance d must equal prelims The magnifying power of a telescope is 9. When it is adjusted for parallel rays the distance between the objective and eyepiece is 20 cm.

The focal length of lenses are Prelims For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index Mains A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its end closer to the pole is 20 cm away from the mirror. The length of the image is Mains Which of the following is not due to total internal reflection?

Prelims A biconvex lens has a radius of curvature of magnitude 20 cm. Which one of the following options describe best the image formed of an object of height 2 cm placed 30 cm from the lens? The combination of the prisms produces dispersion without deviation. The angle of the second prism should be Mains A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side.

If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is Mains A lens having foca length f and aperture of diameter d forms an image of intensity I. Focal length of lens and intensity of image now will be respectively prelims The speed of light in media M 1 and M 2 are 1.

A ray of light enters from medium M 1 to M 2 at an incidence angle i. If the ray suffers total internal reflection, the value of i is mains The angle of refraction at the first face i. Two thin lenses of focal lengths f and f are in contact and coaxial. The power of the combination is prelims A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm.

The diameter of the sun is 1. Prelims a 6. A small coin is resting on the bottom of a beaker filled with liquid. A ray of light from the coin travels upto the surface of the liquid and moves along its surface. How fast is the light travelling in the liquid? The refractive index of material will be A microscope is focussed on a mark on a piece of paper and then a slab of glass of thickness 3 cm and refractive index 1.

How should the microscope be moved to get the mark in focus again? A convex lens and a concave lens, each having same focal length of 25 cm, are put in contact to form a combination of lenses. The power in diopters of the combination is A telescope has an objective lens of 10 cm diameter and is situated at a distance of one kilometre from two objects. One of the refracting surfaces of the prism is made a mirror inwards.

A beam of monochromatic light entering the prism from the other face will retrace its path after reflection from the mirrored surface if its angle of incidence on the prism is A beam of light composed of red and green ray is incident obliquely at a point on the face of rectangular glass slab. When coming out on the opposite parallel face, the red and green ray emerge from Choose the correct statement from the following. A convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens.

Then its focal length will A bulb is located on a wall. Its image is to be obtained on a parallel wall with the help of convex lens. The lens is placed at a distance d ahead of second wall, then required focal tength will be Diameter of human eye lens is 2 mm.

What will be the minimum distance between two points to resolve them, which are situated at a distance of 50 meter from eye. For the given incident ray as shown in figure, the condition of total internal refraction of this ray the required refractive index of prism will be Which relation is correct from following?

A source of light is placed 4 m below the surface of liquid. The minimum radius of disc needed so that light is not coming out is, A tall man of height 6 feet, want to see his full image.

Then required minimum length of the mirror will be It is silvered on its plane surface. Find focal length after silvering A piano convex lens is made of refractive index 1. The radius of curvature of the curved surface is 60 cm. The focal length of the lens is Colours appear on a thin soap film and on soap bubbles due to the phenomenon of A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm.

On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature 10 cm be placed in order to have an upright image of the object coincident with it? Light enters at an angle of incidence in a transparent rod of refractive index n.

For what value of the refractive index of the material of the rod the light once entered into it will not leave it through its lateral face whatsoever be the value of angle of incidence? An astronomical telescope of tenfold angular magnification has a length of 44 cm. The focal length of the objective is The frequency, wavelength and velocity of light in the glass slab will be respectively If a convex lens of focal length 80 cm and a concave lens of focal length 50 cm are combined together, what will be their resulting power?

The refractive index of water is 1. What will be the speed of light in water? A ray of light from a denser medium strikes a rare medium as shown in figure. The critical angle would be If f v and f R are the focal lengths of a convex lens for violet and red light respectively and F v and F m are the focal lengths of a concave lens for violet and red light respectively, then we must have If c is the velocity of light in vacuum, the time taken by light to travel this thickness of glass is A lens is placed between a source of light and a wall.

It forms images of area A 1 and A 2 on the wall, for its two different positions. The area of the source of light is In a Fresnel biprism experiment, the two positions of lens give separation between the slits as 16 cm and 9 cm respectively. What is the actual distance of separation? To produce the largest magnification, the focal length of the eyepiece should be In order to cut off all the light, coming out of water surface, minimum diameter of the disc placed on the surface of water is A parallel beam of monochromatic light of wavelength A is incident normally on a single narrow slit of width 0.

The light is focussed by a convex lens on a screen placed in focal plane. The first minimum will be formed for the angle of diffraction equal to Interference was observed in interference chamber where air was present, now the chamber is evacuated, and if the same light is used, a careful I observer will see One of the refractive surface of the prism is polished. A beam of monochromatic light will be retrace its path if its angle of indence over the refracting surface of the prism is The third maximum taking the central maximum as zeroth maximum will be at x equal to A beam of monochromatic light is refracted from vacuum into a medium of refractive index 1.

The wavelength of refracted light will be If the refractive index of glass is 1. Ratio of intensities of two waves are given by 4: 1. Then ratio of the amplitudes of the two waves is



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