Question

1. Unpolarized light of intensity I₀ is incident on three polarizing filters. The axis of the first is vertical, that of the second is 29° from vertical, and that of the third is horizontal. What light intensity emerges from the third filter?  ✕ I₀

_2. A 215 mW horizontally polarized laser beam passes through a polarizing filter whose axis is 23° from vertical. What is the power of the laser beam as it emerges from the filter? in mW

3. Two narrow slits 44 µm apart are illuminated with light of wavelength 600 nm. What is the angle of the m = 2 bright fringe in radians? what is the angle in degrees?

4. A diffraction grating is illuminated simultaneously with red light of wavelength 670 nm and light of an unknown wavelength. The fifth-order maximum of the unknown wavelength exactly overlaps the fourth-order maximum of the red light. What is the unknown wavelength? in nm

Answer 1

1)      After the initially unpolarized light passes through the first sheet, the intensity of the light when it emerges from that sheet is

I₀ / 2

. Then after it passes through the second, sheet the intensity becomes

( I₀/2)x(cos(29))². For the last sheet, the angle between the polarized light and the direction of polarization is (90 - 29)=61degrees.

So, the intensity when it emerges from the third sheet is .2350(I₀ / 2)x(cos(61))²

. After approximating (cos(61))², you should get that the intensity is approximately .17975*(I₀ / 2).

2)     P=215 cos(23)

         =197.9 mw

3) Displacement y = (Order m x Wavelength x Distance D)/(slit separation d)

m=2
For double slit separation d =44 micrometers

and light wavelength λ =600 nm

on a screen at distance D = 100 cm

the displacement from the centerline for maximum intensity will be

y = m λ D / d

=(2x600x10^-9x100)/(44x10^-6)

=2.727272 cm
This corresponds to an angle of θ

4)   d sinθ =m λ

So, dsinθ_red = 4x670nm

Also, d sin θ = 5λ

However, if they overlap, then

dsinθ_red=d sinθ_?

4x670nm=5λ_?

Therefore λ=(4x670nm)/5

=536 nm