Two pieces of optically flat glass (n = 1.50) touch at one edge and a separated by a thin stretched fiber at the opposite edge. Light of wavelength 500 nm is shone from above and 100 dark fringes are counted. How thick is the fiber?
A)13 μm
B)100 μm
C)5 μm
D)50 μm
E)25 μm

Question

Quizplus · Accepted Answer

The thickness of the fiber can be calculated using the formula for the thickness of a thin film causing interference: $ t = \frac{m \lambda}{2n} $, where $ m $ is the number of dark fringes, $ \lambda $ is the wavelength of light, and $ n $ is the refractive index. Substituting the given values: $ t = \frac{100 \times 500 \times 10^{-9}}{2 \times 1.5} = 25 \times 10^{-6} $ meters, or 25 μm.

Two Pieces of Optically Flat Glass (N = 1