SOLUTIONS FOR PROBLEMS 4-7

Homwork Set 2 (1/27/97):

Problem 4: Polarization. The electric field vector of an incident linearly polarized light wave makes an angle of +30 degrees with the horizontal fast axis of a quarter-wave plate. Describe, in detail, the state of polarization of the emergent wave.

E_x = E cos 30

E_y = E sin 30

E_x > E_y so get elliptical polarization with ellipse' major axis along x axis.

E_x (fast axis) leads E_y (slow axis) by p/2 so first E_x emerges, then E_y; so CCW or left- handed rotation.

Problem 5: Fizeau Fringes. Fringes are observed when a parallel beam of light of wavelength 500 nm is incident perpendicularly onto a wedge-shaped film with an index of refraction of 1.5. What is the angle of the wedge if the fringe separation is 0.333 cm ?

l_f = l_o/n_f

q = Dy/d = l_o/(2n_fd) = 5 x 10^-5 rad.

Problem 6: Grating Orders. Light with a frequency of 4.0 x 10¹⁴ Hz is incident on a grating formed with 10,000 lines per centimeter. What is the highest-order spectrum that can be seen with this device? Explain.

a = (1/10,000) cm

l = c/f where c is speed of light

a sin q_m = ml

maximum value of sin q = 1

so m_max = a/l = 1.3

need integer value, so m_max = 1

Therefore only the first order can be seen

Problem 7: Diffraction from a square aperture. Imagine that you are looking through a piece of square woven cloth at a point source ( l_o = 600 nm) 20 m away. If you see a square arrangement of bright spots located about the point source, each separated by an apparent nearest-neighbor distance of 12 cm, how close together are the strands of cloth?

d sin q_m = ml

set m = 1

q = sin q = y/L

d = Ll/y = 1 x 10^-4 m = 0.1 mm