When the successive polarizing sheet is rotated by an angle with respect to the preceding sheet, the pane of vibration is rotated by the angle . So if polarizing sheets are stacked with their characteristic angles rotated by angle with respect to the preceding sheet, the plane of vibration will get rotated by angle . Therefore, the plane of vibration of polarized light can be rotated by by stacking polarizing sheets such that

.

(b)

Intensity of light changes after each such rotation of the plane of vibration by a factor of . Let be the intensity of the incident polarized light. The intensity after passing through polarizing sheets will become

.

We want to find the minimum number of sheets required in order for the total intensity loss to be less than 5.0%. That is

.

The answer to the problem can be found by solving the following equation for :

We expect , and to be small so that we may approximate

We thus obtain an algebraic equation from which can be solved, which is

So with 50 polarizing sheets, each rotated by an angle with respect to the preceding sheet plane of vibration of polarized light can be rotated by and at the same it can be ensured that the total intensity loss will be less than 5.0%.