Final answer:
When unpolarized light falls on two polarizing sheets, the angle between the characteristic directions of the sheets must be 35° in order for the intensity of the final transmitted light to be one-third of the maximum intensity of the first transmitted beam.
Step-by-step explanation:
When unpolarized light falls on two polarizing sheets placed one on top of the other, the intensity of the transmitted light depends on the angle between the characteristic directions of the sheets. Let's assume the maximum intensity of the first transmitted beam is represented by I. To find the angle between the characteristic directions, we need to determine the fraction of the intensity of the final transmitted light.
Given that the intensity of the final transmitted light is one-third of the maximum intensity (I/3), we can set up the equation:
I/3 = I*cos²(theta)
Where theta is the angle between the characteristic directions of the sheets.
Simplifying the equation:
cos²(theta) = 1/3
cos(theta) = sqrt(1/3)
theta = arccos(sqrt(1/3))
Using a calculator, we find that theta is approximately 35°.
Therefore, the angle between the characteristic directions of the sheets must be 35°.