In a Young's double-slit experiment, a thin sheet of mica is placed over one of the two slits. As a result, the center of the fringe pattern (on the screen) shifts by an amount corresponding to 30 dark bands. The wavelength of the light in this experiment is 480 nm and the index of the mica is 1.60. The mica thickness is:
A) 0.090 mm
B) 0.012 mm
C) 0.014 mm
D) 0.024 mm
E) 0.062 mm

Question

Quizplus · Accepted Answer

The shift in the fringe pattern is due to the additional optical path length introduced by the mica. The optical path difference is given by (n - 1)t, where n is the refractive index and t is the thickness. This path difference corresponds to 30 dark bands, or 30 wavelengths. Therefore, (1.60 - 1)t = 30 * 480 nm. Solving for t gives t = 0.024 mm.

In a Young's Double-Slit Experiment, a Thin Sheet of Mica