Physics
Chapter 19
· The displacement from equilibrium caused by a wave on a string is given by y(x, t) = (−0.00185 m)sin[(42.8 m−1)x − (744 s−1)t]. For this wave, what are the following? (a) amplitude? (b) number of waves in 1 m? (c) number of complete cycles in 1 s? (d) wavelength? (e) speed? Ans:- 0.00185 m, 6.81 waves, 118 cycles, 0.147 m, 17.4 m/s.
· Point A in the figure is 30 cm below the ceiling. Determine how much longer it will take for a wave pulse to travel along wire 1 than along wire 2. Ans:-2.28
· Show that the function D = A ln(x + vt) is a solution of the wave equation,
(d2D/dt2) = υ2(d2D/dx2)
· A string with linear mass density of 0.1 kg/m is under a tension of 107 N. How much power must be supplied to the string to generate a sinusoidal wave of amplitude 3 cm and frequency 116 Hz? Ans:-782 W
· 15.42. A cowboy walks at a pace of about two steps per second, holding a glass of diameter 11 cm that contains milk. The milk sloshes higher and higher in the glass until it eventually starts to spill over the top. Determine the maximum speed of the waves in the milk. Ans:- 0.44 m/s
· A 49-cm-long wire with a mass of 10.8 g is under a tension of 55.5 N. Both ends of the wire are held rigidly while it is plucked. (a) What is the speed of the waves on the wire? (b) What is the fundamental frequency of the standing wave? (c) What is the frequency of the third harmonic? Ans:- 55.5 m/s, 51.2 Hz, 154 Hz
· Consider a guitar string stretching 84.6 cm between its anchored ends. The string is tuned to play middle C, with a frequency of 256 Hz, when oscillating in its fundamental mode, that is, with one antinode between the ends. If the string is displaced 1.84 mm at its midpoint and released to produce this note, what are the wave speed, v, and the maximum speed, Vmax, of the midpoint of the string? Ans:- 433 m/s, 5.92 m/s
· The tension in a 2.9-m-long, 1.1-cm-diameter steel cable (ρ = 7800 kg/m3) is 810 N. What is the fundamental frequency of vibration of the cable? Ans:- 5.7 Hz
chapter 20
· You drop a stone down a well that is 6.65 m deep. How long is it before you hear the splash? The speed of sound in air is 343 m/s. Ans:- 1.18 s.
· A plane flies at Mach 1.5, and its shock wave reaches a man on the ground 21 s after the plane passes directly overhead. (a) What is the Mach angle? (b) What is the altitude of the plane? The speed of the plane is 514.5 m/s. Ans:- 41.8 degree, 9.66 km
· A standing wave in a pipe with both ends open has a frequency of 444 Hz. The next higher harmonic has a frequency of 626 Hz. (a) Determine the fundamental frequency. (b) How long is the pipe? Ans:- 182 Hz, 0.942 m.
· An observer stands between two sound sources. Source A is moving away from the observer, and source B is moving toward the observer. Both sources emit sound of the same frequency. If both sources are moving with a speed, vsound/9, what is the ratio of the frequencies detected by the observer? Ans:- 0.8
· At a distance of 29 m from a sound source, the intensity of the sound is 62 dB. What is the intensity (in dB) at a point 1.9 m from the source? Assume that the sound radiates equally in all directions from the source. Ans:- 85.7 dB
· A source traveling to the right at a speed of 10.80 m/s emits a sound wave at a frequency of 110.0 Hz. The sound wave bounces off of a reflector, which is traveling to the left at a speed of 5.15 m/s. What is the frequency of the reflected sound wave detected by a listener back at the source? (Use 343 m/s as the speed of sound.) Ans:- 121 Hz
Chapter 21
1) How many electrons do 6.94 kg of water contain?
2) Two identically charged particles separated by a distance of 7.8 m repel each other with a force of 9 N. What is the magnitude of the charges?
3) In solid sodium chloride (table salt), chloride ions have one more electron than they have protons, and sodium ions have one more proton than they have electrons. These ions are separated by about 0.28 nm. Calculate the electrostatic force between a sodium ion and a chloride ion.
4) In gaseous sodium chloride, chloride ions have one more electron than they have protons, and sodium ions have one more proton than they have electrons. These ions are separated by about 0.24 nm. Suppose a free electron is located 0.86 nm above the midpoint of the sodium chloride molecule. What are the magnitude and the direction of the electrostatic force the molecule exerts on it? (Assume the chloride ion lies on the +x-axis and the sodium ion lies on the −x-axis, with the origin as the midpoint between the two ions. The free electron lies on the +y-axis.)
5) Identical point charges Q are placed at each of the four corners of a rectangle measuring 8.0 m by 9.0 m. If Q = 26 µC, what is the magnitude of the electrostatic force on any one of the charges?
6) Charge q1 = 1.1 10-8 C is placed at the origin. Charges q2 = -1.3 10-8 C and q3 = 2.6 10-8 C are placed at points (0.18 m, 0 m) and (0 m, 0.24 m), respectively, as shown in the figure. Determine the net electrostatic force (magnitude and direction) on charge
q3.
7) A small ball with a mass of 10 g and a charge of -0.2 µC is suspended from the ceiling by a string. The ball hangs at a distance of 5.0 cm above an insulating floor. If a second small ball with a mass of 60 g and a charge of 0.4 µC is rolled directly beneath the first ball, will the second ball leave the floor?
8) Four point charges, q, are fixed to the four corners of a square that is 15.0 cm on a side. An electron is suspended above a point at which its weight is balanced by the electrostatic force due to the four point charges, at a distance of 13 nm above the center of the square. (The square is horizontally flat, and the electron is suspended 13 nm vertically above the center of the square.) What is the magnitude of each fixed charge in coulombs? What is the magnitude of each fixed charge as a multiple of the electron’s charge?
Chapter 22
1) A +1.5-nC point charge is placed at one corner of a square (1.5 m on a side), and a -3.0-nC charge is placed on the corner diagonally opposite. What is the magnitude of the electric field at either of the other two corners?
2) Consider an electric dipole on the x-axis and centered at the origin. At a distance h along the positive x-axis, the magnitude of electric field due to the electric dipole is given by k(2qd)/h3. Find a distance perpendicular to the x-axis and measured from the origin at which the magnitude of the electric field stays the same. (Use the following as necessary: h and d.)
3) A charge per unit length +λ is uniformly distributed along the positive y-axis from y = 0 to y = +a. A charge per unit length −λ is uniformly distributed along the negative y-axis from y = 0 to y = −a. Write an expression for the electric field at a point on the x-axis a distance x from the origin. (Use the following as necessary: k, λ, x, and a.)
4) An electron is observed traveling at a speed of 1.67 107 m/s parallel to an electric field of magnitude 11,360 N/C. How far will the electron travel before coming to a stop? (The mass of electron is 9.109 10-31 kg, and the charge on the electron is 1.602 10-19 C. The electron is moving in the direction opposite to the electric field.)
5) A -7-nC point charge is located at the center of a conducting spherical shell. The shell has an inner radius of 2 m, an outer radius of 4 m, and a charge of +8 nC. (Let the radially outward direction be positive.) (a) What is the electric field at r = 1 m? (Indicate the direction with the sign of your answer.) (b) What is the electric field at r = 3 m? (Indicate the direction with the sign of your answer.) (c) What is the electric field at r = 7 m? (Indicate the direction with the sign of your answer.) (d) What is the surface charge distribution, σ, on the outside surface of the shell? (Indicate the direction with the sign of your answer.)
Chapter 23
1- A metal ball with a mass of 7. 10-6 kg and a charge of +6 mC has a kinetic energy of 2. 108 J. It is traveling directly at an infinite plane of charge with a charge distribution of +5 C/m2. If it is currently 1 m away from the plane of charge, how close will it come to the plane before stopping? Ans:- 0.882 m
2- A proton gun fires a proton from midway between two plates, A and B, which are separated by a distance of 83.0 cm; the proton initially moves at a speed of 135.0 km/s toward plate B. Plate A is kept at zero potential, and plate B at a potential of 400.0 V. (a) Will the proton reach plate B? (b) If not, where will it turn around? (If the proton reaches plate B, enter 0.830 m, the distance between the plates.) (c) With what speed will it hit plate A? (If the proton reaches plate B, enter 0.) Ans:- No. 0.612 m, 2.38e+05 m/s.
3- Consider a dipole with charge q and separation d. What is the potential a distance x from the center of this dipole at an angle θ with respect to the dipole axis, as shown in the figure? (Do not assume that x » d. Use any variable or symbol stated above along with the following as necessary: k.)
4- Consider an electron in the ground state of the hydrogen atom, separated from the proton by a distance of 0.0529 nm. (a) Viewing the electron as a satellite orbiting the proton in the electrostatic potential, calculate the speed of the electron in its orbit. (b) Calculate an effective escape speed for the electron. (c) Calculate the energy of an electron having this speed. Using this energy, determine the energy that must be given to the electron to ionize the hydrogen atom. Ans:- 2.19e+06 m/s; 3.10e+06 m/s; 4.36e-18 J; 13.6 eV
5- An electric field varies in space according to this equation: E = E0xe−x. (a) For what value of x does the electric field have its largest value, xmax? (Use the following as necessary: E0.) (b) What is the potential difference between the points at x = 0 and x = xmax? (State an expression for the difference V(xmax) – V(0). Use the following as necessary: E0.) Ans:- 1.
6- An infinite plane of charge has a uniform charge distribution of +5 nC/m2 and is located in the yz-plane at x = 0. A +24 nC fixed point charge is located at x = +1 m. (a) Find the electric potential V(x) on the x-axis from 0 < x < +1 m. (Use the following as necessary: x, k, σ for the surface charge distribution, and q and x0 for the charge and position of the point charge, respectively. Do not substitute numerical values; use variables only.) (b) At what position(s) on the x-axis between x = 0 and x = +1 m is the electric potential a minimum? (Enter your answers from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks.)
7- The electric field, (), and the electric potential, V(), are calculated from the charge distribution, ρ(), by integrating Coulomb’s Law and then the electric field. In the other direction, the field and the charge distribution are determined from the potential by suitably differentiating. Suppose the electric potential in a large region of space is given by V(r) = V0 exp (−r2/a2), where
|
V0 and a are constants and r =
|
x2 + y2 + z2 |
is the distance from the origin. (a) Find the electric field () in this region. (Use the following as necessary: V0, r, a, and ε0.) (b) Determine the charge density ρ() in this region, which gives rise to the potential and field. (Use the following as necessary: V0, r, a, and ε0.) (c) Find the total charge in this region. (Use the following as necessary: V0, r, a, and ε0.) (d) Roughly sketch the charge distribution that could give rise to such an electric field.
8- Two metal balls of mass m1 = 6 g (diameter = 6 mm) and m2 = 7 g (diameter = 7 mm) have positive charges of q1 = 1 nC and q2 = 8 nC, respectively. A force holds them in place so that their centers are separated by 8 mm. What will their velocities be after the force is removed and a large distance separates them? (Enter the magnitudes of the velocities.) Ans:- 0.0402 m/s; 0.0344 m/s
9- A charge of 0.520 nC is placed at x = 0. Another charge of 0.140 nC is placed at x1 = 10.9 cm on the x-axis. (a) What is the combined electrostatic potential of these two charges at x = 20.1 cm, also on the x-axis? (b) At which point(s) on the x-axis does this potential have a (local) minimum? (Enter your answers from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks. If you need to use or –, enter INFINITY or –INFINITY, respectively.) Ans:- 36.9 V; -Infinity; 7.18 cm; Infinity.
Chapter 24
1- A spherical capacitor is made from two thin concentric conducting shells. The inner shell has radius r1, and the outer shell has radius r2. What is the fractional difference in the capacitances of this spherical capacitor and a parallel plate capacitor made from plates that have the same area as the inner sphere and the same separation d = r2 − r1 between plates? (Use the following as necessary: r1, r2, and ε0.)
2- Four capacitors with capacitances C1 = 3.4 nF, C2 = 2.2 nF, C3 = 1.6 nF, and C4 = 5.3 nF are wired to a battery with V = 10.3 V, as shown in the figure. What is the equivalent capacitance of this set of capacitors?
3- A potential difference of V = 80.0 V is applied across a circuit with capacitances C1 = 14.5 nF, C2 = 4.00 nF, and C3= 26.5 nF, as shown in the figure. What is the magnitude and sign of q3l, the charge on the left plate of C3 (marked by point A)? What is the electric potential, V3, across C3? What is the magnitude and sign of the charge q2r, on the right plate of C2 (marked by point B)?
4- Fifty-two parallel plate capacitors are connected in series. The distance between the plates is d for the first capacitor, 2d for the second capacitor, 3d for the third capacitor, and so on. The area of the plates is the same for all the capacitors. Express the equivalent capacitance of the whole set in terms of C1 (the capacitance of the first capacitor).
5- A 7000-nF parallel plate capacitor is connected to a 2.4-V battery and charged. (a) What is the charge Q on the positive plate of the capacitor? (b) What is the electric potential energy stored in the capacitor? The 7000-nF capacitor is then disconnected from the 2.4-V battery and used to charge three uncharged capacitors, a 100-nF capacitor, a 200-nF capacitor, and a 300-nF capacitor, connected in series. (c) After charging, what is the potential difference across each of the four capacitors? d) How much of the electrical energy stored in the 7000-nF capacitor was transferred to the other three capacitors?
7- A proton traveling along the x-axis at a speed of 5.0 106 m/s enters the gap between the plates of a 4.0-cm-wide parallel plate capacitor. The surface charge distributions on the plates are given by σ = ±1.0 10-6 C/m2. How far has the proton been deflected sideways (Δy) when it reaches the far edge of the capacitor? Assume that the electric field is uniform inside the capacitor and zero outside. (The plates of the capacitor are parallel to the x-axis. The charge of the proton is +1.602 10-19 C and the mass of the proton is 1.67 10-27 kg.)
Chapter 25
1- A copper wire has a diameter dCu = 0.0470 cm, is 3.00 m long, and has a density of charge carriers of 8.50 x1028 electrons/m3. As shown in the figure, the copper wire is attached to an equal length of aluminum wire with a diameter dAl = 0.0110 cm and density of charge carriers of 6.02 x1028 electrons/m3. A current of 0.470 A flows through the copper wire. (a) What is the ratio of the current densities in the two wires, JCu/JAl? (b) What is the ratio of the drift velocities in the two wires, vd-Cu/vd-Al?
2- As illustrated in the figure, a current, i, flows through the junction of two materials with the same cross-sectional area and with conductivities σ1 and σ2. Show that the total amount of charge at the junction is ε0i(1/σ2 − 1/σ1).
3- A 10-gauge copper wire, with a constant potential difference of 0.4 V applied across its 1 m length at room temperature (20° C), is cooled to liquid nitrogen temperature (77 K = −196 °C). (The resistivity and temperature coefficient of resistivity of copper are 1.72 10-8 m Ω and 3.9 10-3 K−1, respectively.) (a) Determine the percentage change in the wire’s resistance during the drop in temperature. (b) Determine the percentage change in current flowing in the wire. (c) Compare the drift speeds of the electrons at the two temperatures. (Copper has 1 conducting electron per atom.)
4- What is the equivalent resistance of the five resistors in the circuit in the figure? Let R1 = 28 Ω, R2 = 56 Ω, R3 = 84 Ω, R4 = 112 Ω, R5 = 140 Ω. (When entering units, use ohm for Ω.)
5- A potential difference of V = 0.550 V is applied across a block of silicon with resistivity 8.70 10-4 Ω m. As indicated in the figure, the dimensions of the silicon block are width a = 2.00 mm and length L = 18.5 cm. The resistance of the silicon block is 50.0 Ω, and the density of charge carriers is 1.23 1023 m-3. Assume that the current density in the block is uniform and that current flows in silicon according to Ohm’s Law. The total length of 0.500-mm-diameter copper wire in the circuit is 78.0 cm, and the resistivity of copper is 1.69 10-8 Ω m. (a) What is the resistance, Rw, of the copper wire? (b) What are the direction and the magnitude of the electric current, i, in the block? (Indicate the direction in the block as displayed in the figure above.) (c) What is the thickness, b, of the block? (d) On average, how long does it take an electron to pass from one end of the block to the other? (e) How much power, P, is dissipated by the block? (f) In what form of energy does this dissipated power appear?
Chapter 26
1- Find the equivalent resistance for the circuit in the figure. (Use the following as necessary: Vemf, R.)
2- The dead battery of your car provides a potential difference of 9.630 V and has an internal resistance of 1.150 Ω. You charge it by connecting it with jumper cables to the live battery of another car. The live battery provides a potential difference of 12.00 V and has an internal resistance of 0.0100 Ω, and the starter resistance is 0.0700 Ω. (a) Draw the circuit diagram for the connected batteries. (The starter is in parallel with the live battery.) (Do this on paper. Your instructor may ask you to turn in this work.) (b) Determine the current in the live battery, in the dead battery, and in the starter immediately after you closed the circuit.
3- The circuit shown in the figure consists of two batteries with VA = 6.3 V and VB = 12.1 V and three light bulbs with resistances R1, R2, and R3. Calculate the magnitudes of the currents i1, i2, and i3 flowing through the bulbs.
4- A circuit consists of two 3.45-kΩ resistors in series with an ideal 12.0-V battery. (a) Calculate the current flowing through each resistor. (b) A student trying to measure the current flowing through one of the resistors inadvertently connects an ammeter in parallel with that resistor rather than in series with it. How much current will flow through the ammeter, assuming that it has an internal resistance of 2.5 Ω?
5- What is the time constant for the discharging of the capacitors in the circuit shown in the figure? If the 2-µF capacitor initially has a potential difference of 63 V across its plates, how much charge is left on it after the switch has been closed for a time equal to half of the time constant?
6- A 6.0-V battery is attached to a 6-mF capacitor and a 440-Ω resistor. Once the capacitor is fully charged, what is the energy stored in it? What is the energy dissipated as heat by the resistor as the capacitor is charging?
Chapter 27
· Determine the force on a semicircular wire with current I in the presence of a field B.
·
· A conducting rod of length L slides freely down an inclined plane, as shown in the figure. The plane is inclined at an angle θ from the horizontal. A uniform magnetic field of strength B acts in the positive y-direction. Determine the magnitude and the direction of the current that would have to be passed through the rod to hold it in position on the inclined plane. (Use any variable or symbol stated above along with the following as necessary: g. Indicate your direction based on the side view.)
A copper wire with density ρ = 8960 kg/m3 is formed into a circular loop of radius 47.0 cm. The cross-sectional area of the wire is 1.00 10-5 m2, and a potential difference of 0.020 V is applied to the wire. What is the maximum angular acceleration of the loop when it is placed in a magnetic field of magnitude 0.20 T? The loop rotates about an axis through a diameter. (Use 1.72 10-8 Ω m for the resistivity of copper.)
Chapter 28
·
· The figure below shows a Helmholtz coil used to generate uniform magnetic fields. Suppose the Helmholtz coil consists of two sets of coaxial wire loops with 13 turns of radius R = 71.0 cm, which are separated by R, and each coil carries a current of 0.134 A flowing in the same direction. Calculate the magnitude and the direction of magnetic field in the center between the coils.
· What is the magnitude of the magnetic field inside a long, straight tungsten wire of circular cross section with diameter 3.6 mm and carrying a current of 2.7 A, at a distance of 0.5 mm from its central axis? (The magnetic suspect
Chapter 29 Class Problem
· A circular conducting loop with radius a and resistance R2 is concentric with a circular conducting loop with radius b » a (b much greater than a) and resistance R1. A time-dependent voltage is applied to the larger loop, having a slow sinusoidal variation in time given by V(t) = V0 sin ωt, where V0 and ω are constants with dimensions of voltage and inverse time, respectively. Assuming that the magnetic field throughout the inner loop is uniform (constant in space) and equal to the field at the center of the loop, derive expressions for the potential difference induced in the inner loop and the current i through that loop. (Use the following as necessary: a, b, R1, R2, V0, ω, t, and μ0.)
· The conducting loop in the shape of a quartercircle shown in the figure has a radius of 20 cm and resistance of 0.8 Ω. The magnetic field strength within the dotted circle of radius 6 cm is initially 5 T. The magnetic field strength then decreases from 5 T to 1 T in 7 s. (a) Find the magnitude of the induced current in the loop. (b) Find the direction of the induced current in the loop.
· A short coil with radius R = 18 cm contains N = 30 turns and surrounds a long solenoid with radius r = 3.0 cm containing n = 60 turns per centimeter. The current in the short coil is increased at a constant rate from zero to i = 1.5 A in a time of t = 16 s. Calculate the induced potential difference in the long solenoid while the current is increasing in the short coil.
· In the circuit in the figure, a battery supplies Vemf = 10 V and R1 = 4.0 Ω, R2 = 4.0 Ω, and L = 2.0 H. Calculate each of the following a long time after the switch is closed. (a) the current flowing out of the battery. (b) the current through R1; (c) the current through R2; (d) the potential difference across R1; (e) the potential difference across R2; (f) the potential difference across L; (g) the rate of current change across R1.
· An emf of 30 V is applied to a coil with an inductance of 34 mH and a resistance of 0.70 Ω. (a) Determine the energy stored in the magnetic field when the current reaches one fourth of its maximum value. (b) How long does it take for the current to reach this value?
Q. An emf of 24.0 V is applied to a coil with an inductance of 58.0 mH and a resistance of 0.41 Ω.
a) Determine the energy stored in the magnetic field when the current reaches one fourth of its maximum value.
b) How long does it take for the current to reach this value?
Answer: a)The maximum current, after a long time has elapsed, will be 24/0.41 = 58.5A. A quarter of this is 14.63A. Energy stored in an inductor is 0.5*L*I^2 = 6.21J
b) you can use I(t)/ Imax =1 – exp(-t*R/L) where I(t) is the current at time t (14.63A), Imax is the maximum current (58.5A), R is the resistance, L the inductance
0.75 = exp(-t*7.07)
t*7.07= 0.288
t = 40.7ms
· A motor has a single loop inside a magnetic field of magnitude 0.95 T. If the area of the loop is 200. cm2, find the maximum angular speed possible for this motor when connected to a source of emf providing 210 V.
Chapter 30
· 30.27. A 18-µF capacitor is fully charged by a 12-V battery and is then disconnected from the battery and allowed to discharge through a 0.9-H inductor. Find the first three times when (the magnitude of) the charge on the capacitor is 78-µC, taking t = 0 as the instant when the capacitor is connected to the inductor.
· 30.31. A 2.10-µF capacitor was fully charged by being connected to a 12.0-V battery. The fully charged capacitor is then connected in series with a resistor and an inductor: R = 53 Ω and L = 0.240 H. Calculate the damped frequency of the resulting circuit.
· 30.50. A circuit contains a 100-Ω resistor, a 0.0510-H inductor, a 0.450-µF capacitor, and a source of time-varying emf connected in series. The time-varying emf is 55.0 V at a frequency of 2000 Hz. (a) Determine the current in the circuit. (b) Determine the voltage drop across each component of the circuit. (c) How much power is drawn from the source of emf?
· 30.54. A transformer has 820 turns in the primary coil and 34 turns in the secondary coil. (a) What happens if an AC voltage of 100 V is across the primary coil? (What is the voltage across the secondary coil?) (b) If the initial AC current is 2 A, what is the output current? (c) What happens if a DC current at 100 V flows into the primary coil? (What is the voltage across the secondary coil?) (d) If the initial DC current is 2 A, what is the output current?
Chapter 31
· A wire of radius 1.0 mm carries a current of 21.0 A. The wire is connected to a parallel plate capacitor with circular plates of radius R = 3.1 cm and a separation between the plates of s = 2.0 mm. What is the magnitude of the magnetic field due to the changing electric field at a point that is a radial distance of r = 1.0 cm from the center of the parallel plates? Neglect edge effects. (Assume the current has just begun charging the capacitor.) Ans:- 4.37e-05 T
· A laser produces light that is polarized in the vertical direction. The light travels in the positive y-direction and passes through two polarizers, which have polarizing angles of 35° and 55° from the vertical, as shown in the figure. The laser beam is collimated (neither converging nor expanding), has a circular cross section with a diameter of 1.70 mm, and has an average power of 16 mW at point A. At point C, what are the magnitudes of the electric and magnetic fields, and what is the intensity of the laser light? Ans:- 1770 V/m, 5.92e-06 T, 4180 W/m^2
· A microwave operates at 565 W. Assuming that the waves emerge from a point source emitter on one side of the oven, how long does it take to melt an ice cube 2 cm on a side that is 10 cm away from the emitter if 10% of the photons are absorbed by the cube? Assume a cube density of 0.96 g/cm3. (Also assume that the ice cube is initially at 0°C but has not yet started melting, and that the ice cube maintains its shape until it absorbs enough energy to completely melt.) How many photons of wavelength 10 cm hit the ice cube per second? Ans:- 3.97 hr, 9.05e+23 photon/sec
Chapter 32 practice Problems
· A single concave spherical mirror is used to create an image of a source 6.80 cm tall that is located at position x = 0 cm which is xo = 18.0 cm to the left of Point C, the center of curvature of the mirror, as shown in the figure. The magnitude of the radius of curvature for the mirror is R = 13.5 cm. Calculate the position xi where the image is formed. Use the coordinate system given in the drawing. What is the height hi of the image? Is the image upright or inverted (upright = pointing up, inverted = pointing down)? Is it real or virtual? Ans:- 22.9 cm, 1.85 cm, inverted, real
· A ray of light is incident on an equilateral triangular prism with an index of refraction of 1.29. The ray is parallel to the base of the prism when it approaches the prism. The ray enters the prism at the midpoint of one of its sides, as shown in the figure. What is the direction of the ray when it emerges from the triangular prism? Ans:- 21.2 degree
· In a step-index fiber, the index of refraction undergoes a discontinuity (jump) at the core-cladding interface, as shown in the figure. Infrared light with wavelength 1530 nm propagates through such a step-index fiber through total internal reflection at the core-cladding interface. The index of refraction for the core at 1530 nm is ncore = 1.48. If the maximum angle αmax at which light can be coupled into the fiber such that no light will leak into the cladding is αmax = 13.832°, calculate the percent difference between the index of refraction of the core and the index of refraction of the cladding. (Let dcore = 9 µm and dcladding = 125 µm.) Ans:- 1.31. %
· Refer to the figure below and prove that the arc of the primary rainbow represents the 42° angle from the direction of the sunlight.
· A concave mirror forms a real image twice as large as the object. The object is then moved such that the new real image produced is three times the size of the object. If the image was moved 69.0 cm from its initial position, how far was the object moved? What is the focal length of the mirror? Ans:- 11.5 cn, 69 cm
· How deep does a point in the middle of the floor of a 3-m-deep pool appear to a person standing 3.3 meters horizontally from the point? Take the refractive index for the pool to be 1.3 and for air to be 1. (Assume the person is standing in the pool with their eyes just above the level of the water.) Ans:-0.938 m
Chapter 33 practice Problems
· Demonstrate that the minimum distance possible between a real object and its real image through a thin convex lens is 4f, where f is the focal length of the lens.
· An air-filled cavity bound by two spherical surfaces is created inside a glass block. The two spherical surfaces have radii R1 = 34.4 cm and R2 = 21.0 cm, respectively, and the thickness of the cavity is d = 41.2 cm (see diagram below). A light-emitting diode (LED) is embedded inside the block a distance of 60.0 cm in front of the cavity. Given nglass = 1.50 and nair = 1.00, and using only paraxial light rays (i.e., in the paraxial approximation) do the following. (The paraxial approximation is a small angle approximation so sin(θ) ≈ θ. This applies to both the incident angles and refracted angles.) (a) Calculate the final position of the image of the LED through the air-filled cavity. (b) Draw a ray diagram showing how the image is formed. Ans:- 48.2 cm, to the left of the second surface.
· Two lenses are used to create an image for a source 10.0 cm tall that is located at do = 31.0 cm to the left of the first lens, as shown in the figure below. Lens L1 is a biconcave lens made of crown glass (index of refraction n = 1.55) and has a radius of curvature of 20.0 cm for both surface 1 and 2. Lens L2 is d = 39.0 cm to the right of the first lens L1. Lens L2 is a converging lens with a focal length f = 30.5 cm. At what distance relative to the object does the image get formed? Determine this position by sketching rays and calculating algebraically. Ans:- 77.1 cm, to the right of lens L2
· Some reflecting telescope mirrors utilize a rotating tub of mercury to produce a large parabolic surface. If the tub is rotating on its axis with an angular frequency ω, show that the focal length of the resulting mirror is: f = g/2ω2.
· Jack has a near point of 30.2 cm and uses a magnifier of 27.0 diopter. (a) What is the magnification if the final image is at infinity? (b) What is the magnification if the final image is at the near point? Ans:- 8.15, 9.15.
· A diverging lens with f = −28.0 cm is placed 16.1 cm behind a converging lens with f = 21.6 cm. Where will an object at infinity in front of the converging lens be focused? Ans:- 6.84 cm
Chapter 34
1- Coherent monochromatic light with wavelength λ = 530 nm is incident on two slits that are separated by a distance d = 0.500 mm. The intensity of the radiation at a screen 2.50 m away from each slit is 168.0 W/cm2. Determine the position y1/3 at which the intensity of the central peak (at y = 0) drops to Imax/3. Ans:- 0.00108 m
· White light (400 nm < λ < 750 nm) shines onto a puddle of water (n = 1.33). There is a thin (109.7 nm thick) layer of oil (n = 1.47) on top of the water. What wavelengths of light would you see reflected? (Enter your answers from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks.) Ans:- 645 nm, none
· Some mirrors for infrared lasers are constructed with alternating layers of hafnia and silica. Suppose you want to produce constructive interference from a thin film of hafnia (n = 1.90) on BK-7 glass (n = 1.51) when infrared radiation of wavelength 1.39 µm is used. What is the smallest film thickness that would be appropriate, assuming the laser beam is oriented at right angles to the film? Ans:- 1.83e-07 m
· Sometimes thin films are used as filters to prevent certain colors from entering a lens. Consider an infrared filter, designed to prevent 847.0-nm light from entering a lens. Find the minimum film thickness for a layer of MgF2 (n = 1.38) to prevent this light from entering the lens. (Assume that nlens < 1.38.) Ans:- 153 nm
· White light shines on a sheet of a material that has a uniform thickness of 1.44 µm. When the reflected light is viewed using a spectrometer, it is noted that light with wavelengths of 499.2 nm, 561.6 nm, 641.8 nm, 748.8 nm, and 898.6 nm is not present in the reflected light. What is the index of refraction of the material? Ans:- 1.56
· A common interference setup consists of a plano-convex lens placed on a plane mirror and illuminated from above at normal incidence with monochromatic light. The pattern of circular interference fringes (fringes of equal thickness)—bright and dark circles—formed due to the air wedge defined by the two glass surfaces, is known as Newton’s rings. In an experiment using a plano-convex lens with focal length f = 80.50 cm and index of refraction nl = 1.500, the radius of the third bright circle is found to be 0.8525 mm. Determine the wavelength of the monochromatic light. Ans:- 7.22e-07 m
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