A single beam of coherent light (? = 633?10-9 m) is incident on two glass slides

Question

A single beam of coherent light (? = 633?10-9 m) is incident on two glass slides (with a refractive index of 1.50), which are touching at one end and are separated by a d = 0.0215-mm thick sheet of paper on the other end, as shown in the figure. Beam 1 reflects off the bottom surface of the top slide, and Beam 2 reflects off the top surface of the bottom slide. Assume that all the beams are perfectly vertical and that they are perpendicular to both slides, i.e., the slides are nearly parallel (the angle is exaggerated in the figure); the beams are shown at angles in the figure so that they are easier to identify. Beams 1 and 2 recombine at the location of the eye in the figure. The slides are L = 8.17 cm long and D = 1.07 mm thick.

a) At what position does the first bright fringe appear?

Explanation / Answer

the first bright fringe occurs where the thickness of the air is a quarter wavelength, or

633 nm / 4 = 158.25 nm

How far from the left end is this?

use similar triangles, i.e. ratios...

distance from left end / thickness there = length of slide / thickness of paper at end

distance from left end / 158.25 nm = 8.17 cm / 21500 nm

dist from left end = 0.060135 cm = 0.60135 mm

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