Light is incident nearly perpendicularly on four layers of thickness L. The inde

Question

Light is incident nearly perpendicularly on four layers of thickness L. The indexes of refraction of the thin layers and of the media above and below these layers are given. Let ? represent the wavelength of the light in air, and n2 represent the index of refraction of the thin film in each situation.

a. For which of the four situations do the reflected beams undergo fully constructive interference and why?

b. For what minimum non-zero thickness of L will the reflected beams in situation (c) interfere constructively when illuminated by a ?v = 660 nm beam?

c. Please draw a ray diagram, using the three main rays. Make sure you use solid lines for the actual rays and dashed lines for their extensions, and that you mark the direction of travel of the rays with an arrow.

Explanation / Answer

(b) and (d) gives constructive interference ;

For constrauctive interference , light rays there shouldn't be phase difference

When light rays get reflected by a surface, a 1800 phase shift is occured if the underneath surface has more refractive index.

for (a) ; there is 1800 phase difference when the light get reflected from the bottom surface.

for (b) there is 1800 phase difference when the light get reflected from the first surface and then again second surface surface. So net phase different=0

for (c); there is 1800 phase difference when the light get reflected from the bottom surface.

for (d); no change in phase when getting reflected.

b. as stated before, for constructive interference phase difference=0 or 360; 180+p = 360 ; p=180

where p- phase shift due to travelling inside the medium

p= (2L/l')*360 ; l'- wavelength in the medium = v / n2 =471.43 nm

(2L/l')*360 =180*(2n+1) ; n is an integer

for minimum L; when n=0

L=117.86 nm

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