## Waves and Optics

• Waves
Sinusoidal traveling waves, superposition and interference, standing waves, reflection, refraction and diffraction, the Doppler effect.
• Electromagnetic Waves
Maxwell's equations, production of EM Waves, polarization, double-slit experiment, interference in thin films, single slit experiment, diffraction grating
• Mirrors and Lenses
Geometric optics, flat mirrors, spherical mirrors, thin lenses, aberrations

### Problem 1:

A certain 100 m length of piano wire has a mass of 1 kg.  If a transverse wave moves on the wire with a speed of 100 m/s, the tension in the wire is closest to

(A)  10 N    (B)  102 N    (C)  103 N    (D)  104 N   (E)  105 N

### Problem 2:

The following functions may represent a wave disturbance in one dimension in terms of position x, time t, and positive constants A, a, and b.  Which function represents a traveling wave moving in the negative x-direction?

(A)  f(x,t) = A sin(ax + bt)
(B)  f(x,t) = A sin(ax - bt)
(C)  f(x,t) = A cos(ax) cos(bt)
(D)  f(x,t) = A sin(ax) sin(bt)
(E)  f(x,t) = A sin(ax) cos(bt)

### Problem 3:

A source of 1 kHz sound is moving straight towards you at a speed 0.9 times the speed of sound.  The frequency you receive is

(A)  0.1 kHz    (B)  0.5 kHz    (C)  1.1 kHz   (D)  1.9 kHz   (E)  10 kHz

(A)  I    (B)  II    (C)  III   (D)  IV   (E)  V

### Problem 4:

A spherical concave mirror is shown in the figure.  The focal point F and the location of the object O are indicated.   At what point will the image be located?

(A)  I    (B)  II    (C)  III   (D)  IV   (E)  V

### Problem 5:

An electromagnetic wave propagates along the y-axis in a medium with index of refraction n.  At time t the equation of the electric field in the medium (in SI units) is
E = E0 sin(5*106 πy - 5*1014 πt + π/6).
The index of refraction of the medium is most nearly

(A)  6    (B)  5    (C)  4   (D)  3   (E)  2

### Problem 6:

Coherent monochromic light passes through two narrow slits and forms an interference pattern on a distant screen.  The space between the slits is filled with media having different indices of refraction, n1 and n2, as shown in the figure.  Light from slit 1 travels a distance L1, passing only through medium 1.  Light from slit 2 travels a distance L2, passing only through medium 2 to reach the same point.  What is a possible relationship between L1 and L2?

(A)  L1 = (n1/n2) L2    (B)  (n1/n2)½ L2    (C)  (n2/n1) L2   (D)  (n2/n1)½ L2   (E)  (1 + n1/n2) L2

### Problem 7:

Radio waves emanating from a distant quasar at a frequency of 30 GHz are received with a dish antenna 10 m in diameter.  With what precision can the direction of the quasar be determined?

### Problem 8:

Unpolarized light of intensity I0 traveling in the +z-direction passes successively through 3 perfect polarizers.  The first of these passes light polarized along the x-axis, the middle one passes light polarized at an angle θ relative to the x-axis, and the last one passes light polarized along the y-axis.  The intensity of the light emerging from the third polarizer is

(A)  0    (B)  ½I0   (C)  ½I0 sin2θ   (D)  I0 cos2θ    (E)  (1/8)I0 sin2(2θ)

### Problem 9:

A slit of vertical height 1*10-4 m and horizontal width 4*10-4 m is a distance 1 m from a screen as shown in the figure.  Light of wavelength 500 nm is incident on the slit.  At the screen the pattern consists of a

(A)  vertical line of dots.
(B)  horizontal line of dots.
(C)  grid of dots with the vertical spacing 4 times larger than the horizontal spacing.
(D)  grid of dots with the vertical spacing 4 times smaller than the horizontal spacing.
(E)  grid of dots with equal vertical and horizontal spacing.

### Problem 10:

An anti-reflection coating with index of refraction 1.25 is put on glass with index of refraction 1.56.  If the coating is designed for light incident normally on the glass with wavelength 400 nm in air, which of the following thicknesses of the coating will result in minimum reflection?

(A)  4 nm    (B)  80 nm   (C)  160 nm   (D)  320 nm    (E)  640 nm