Question

Thanks So much in advance!

1. Unpolarized light with an intensity of 510 W / m² is incident on a polarizer with an unknown axis. The light then passes through a second polarizer with has an axis which makes an angle of 77.5° with the vertical. After the light passes through the second polarizer, its intensity has dropped to 188 W / m². What is the angle between the axes of the polarizers?

2.Unpolarized light of intensity I₀ is incident on three polarizing filters. The axis of the first is vertical, that of the second is 45° from vertical, and that of the third is horizontal. What light intensity emerges from the third filter?  

Answer 1

(A)

An ideal polarizer produces linearly polarized lightfrom unpolarized light. Two ideal polarizers would eliminate all light

if their transmission directions are placed at right angles

Applying the law of malus

(I(final)=I(initial)*(cos(theta))^2 )

When unpolarized light is incident on a polarizer, it will decrease intensity of its polarity by half i.e, intensity would be

510/2 = 255 W/m^2

188=255(cos(theta))^2

cos(theta)^2 =

So, Theta = 42.50 degrees

angle between the axes of the polarizers is 42.50 degrees

(B)

Fraction getting through first filter is   1/2

Fraction through second filter is cos^2(phi) where (phi) is angle between 1st and 2ndpolarizers... 45 degrees

Fraction through third filter is cos^2(theta) where (theta) is angle between 2nd and3rd filter... 22.5 degrees.

So overall fraction of light emerging = 1/2 * cos^2(45) * cos^2(22.5)

= 0.5 * 0.5 * 0.853

= 0.213