Question

1. Answer these following questions on polarizers and light.

a. A polarized light is incident on several polarizing disks whose planes are parallel and centered on common axis. Suppose that the transmission axis of the first polarizer is rotated 24° relative to the axis of polarization of the incident light, and that the transmission axis of each additional analyzer is rotated 24° relative to the transmission axis of the previous one. What is the minimum number of polarizer needed (whole number), so the transmitted light through all polarizing sheets has an intensity that is less than 9% that striking the first polarizer?

b. Three polarizing disks whose planes are parallel and centered on common axis. The directions of their transmission axes relative to the vertical are respectively: θ1 = 39o clockwise, θ2 = 17o counter-clockwise, and θ3 = 10o clockwise. A beam of light polarized along the vertical is incident onto the first polarizer with an intensity of I0 = 28.0 W/m². Calculate the transmitted intensity through all three polarizers.

c. A 2.4-cm high object is situated 12.5 cm in front of a concave mirror that has a radius of curvature of 8.0 cm. What is the height of the image?

Answer 1

a] From Malus' law, the intensity of light after the polarizer is

here, every polarizer bears an angle of 24 degrees with respect to each other. So,

here, I_n = 9% of I_o

=>

taking log on both sides gives,

log(0.09) = 2nlog(cos24)

=> n = 13.31 or approximately 13.

this is the minimum number of polarizers required.

b] Again, using Malus' law gives,

I = 28(cos²39)(cos²[39+17])(cos²[39+17+10]) = 0.875 W/m².

c] focal length of the mirror = R/2 = 4 cm

use the mirror equation

1/f = 1/v + 1/u

=> 1/4 = 1/v + 1/12.5

=> v = image distance = 5.88 cm

the height of the image will be:

H = magnification x object height = (v/u)(2.4) = 1.13 cm.