2 polarizer are kept crossed and 10 half wave plates are introduced such that each makes pi/40 with prev find?

Question

find intensity of light coming out

Answer 1

Well, you forget to specify whether the incoming light source is polarized or not.
Suppose the incoming light is polarized as the first polarizer. Without the half wave plates, no light would be able to coming out, since the light is pi/2 phase out of the second polarizer.
10* pi/40 = pi/4
After passing the half wave plates, the beam would be pi/2 - pi/4 = pi/ 4 phase out of the second polarizer.
Thus the (transverse) vibration magnitude of the light out would be sqrt(2)/2 of the incoming light. Since the light intensity is proportional to the square of the vibration magnitude, the intensity of light coming out is to be (sqrt(2)/2)^2 = 1/2 of the incoming polarized light intensity.