Homework Problem Set 12
Homework due by 5:00 pm on Thursday April 26.
Partial credit may be given even if the final answer is incorrect so please show all work!
Question 1 (1 point)
What is Rayleigh’s Criterion? What can it be used for?
Solution: Rayleigh’s Criterion for two images to be considered just resolved is that the central
maximum of one image falls on the first minimum of the second image, or θmin = 1.22 λ/D
Question 2 (3 points)
A thin film of oil is placed on the surface of a piece of glass. The oil has an index of refraction of
1.29 and the glass has an index of refraction of 1.56. If the film produces a first-order maximum
of light of wavelength 550 nm normally incident on it, how thick is the film?
Solution: For the first maximum with light normal to the surface we must have 2d = λoil = λ/noil
= (550 nm)/(2 × 1.29) = 213 nm
Question 3 (3 points)
What is the ratio between the intensities of the brightest maximum in a single-slit diffraction
pattern and the second brightest maximum for the same pattern? The brightest maximum is the
same as the central maximum.
Solution: For single slit diffraction we have: I = Imax[sin(π a sinθ / λ)/( π a sinθ / λ)]2
At θ = 0 (the position of the central/brightest maximum) we have simply I = Imax
At the next maximum (which is the second brightest) we have the condition that sin θ = 3/2 (λ/a)
Thus: (I/Imax) = [sin(π a (3/2 (λ/a) /λ)/ π a (3/2 (λ/a) /λ]2 = [sin (3π/2)/ 3π/2]2 = (2/3π)2= 0.045
Question 4 (3 points)
A 720 nm light beam in air hits the flat surface of a certain plastic and the beam is split into a
reflected ray and a refracted ray. If the reflected ray is completely polarized when it is at 39º with
respect to the surface, what is the index of refraction of the plastic?
Solution: The beam is incident at 39º with respect to the surface, thus it is 51º with respect to the
normal. In the case where the reflected beam is completely polarized the refracted beam must be
51º with respect to the surface and 39º with respect to the normal. (See Figure 38.28). In this case
we have simply that n = tan (51º) = 1.23