A plano-convex glass lens of radius of curvature R = 1.5 m rests on an optically

Question

A plano-convex glass lens of radius of curvature R = 1.5 m rests on an optically flat glass plate. The arrangement is illuminated from above with monochromatic light of 513nm wavelength. The indexes of refraction of the lens and plate are 1.6. The condition for a bright (constructive) interference ring is given below for a thickness t.

t = ( m + 1/2 )( /2 ), m = 0, 1, 2, ...

For t << R, the radius of a fringe is related to t as follows.

Determine the radii of the first and second bright fringe in the reflected light.
...... mm (first bright fringe)
.......... mm (second bright fringe)

Explanation / Answer

The condition for a bright (constructive) interference ring is given below for a thickness t.

t = (m + 1/2)/2

For first bright fringe,

m=0 and t1 =513/4 nm = 128.25 nm

For second fringe,

m=1, t2=513 *3/4 =384.75 nm

r1 = sqrt(2×1.5×128.25×10^-9) m

= 0.620 mm

r2 =sqrt(2×1.5×384.75×10^-9) m

= 1.074 mm

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