Three polarizing plates whose planes are parallel are centered on a common axis.

Question

Three polarizing plates whose planes are parallel are centered on a common axis. The directions of the transmission axes relative to the common vertical direction are shown in the figure below. A linearly polarized beam of light with plane of polarization parallel to the vertical reference direction is incident from the left onto the first disk with intensity I_i = 11.0 units (arbitrary). Calculate the transmitted intensity If when theta_1 = 21.0 degree, theta_2 = 43.0 degree, and theta_3 = 61.0 degree. A patient can't see objects closer than 45.2 cm and wishes to clearly see objects that are 20.0 cm from his eye. (a) Is the patient nearsighted or farsighted' (b) If the eye-lens distance is 2.04 cm, what is the minimum object distance p from the lens? (Give your answer to at least three significant digits.) 17.96 cm (c) What image position with respect to the lens will allow the patient to see the object? (Give your answer to at least three significant digits.)

Explanation / Answer

Initial intensity = I0

because light is initially unpolarised, after going through first polariser intensity will halved.

After the first polariser

I1 = Ii/2

After that intensity is reduced by (cos^2 A) factor

A = 43 - 21 = 22 deg

after second polarizer intensity will be I2 = I1*(cos 22 deg)^2

A = 61 - 43 = 18 deg

after 3rd polarizer intensity will be I3 = (I2)*(cos 18 deg)^2

So,

I3 = (Ii/2)*(cos 22 deg)^2*(cos 18 deg)^2

I3 = (11/2)*(cos 22 deg)^2*(cos 18 deg)^2 = 4.28

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