4. In the prism shown, a beam of red light 665 nm is incident at an angle ?1 wit

Question

4. In the prism shown, a beam of red light 665 nm is incident at an angle ?1 with the normal. The glass has an index of refraction of 1.65. When ?1 = 40°, the beam emerges on the other side of the prism at an angle ?4 = 84°.

a. Calculate the angle of refraction ?2 at the left side of the prism.

b. Using the same prism, describe a change to the apparatus that would result in total internal reflection of the beam at the right side of the prism. Justify your answer.

c. The incident beam is now perpendicular to the surface. The glass is coated with a thin film that has an index of refraction 1.38 to reduce the partial reflection of the beam at this angle.

i. Calculate the wavelength of the red light in the film.

ii. Calculate the minimum thickness of the film for which the intensity of the reflected red ray is near zero.

Explanation / Answer

by snell's law

n1 / n2 = sin(theta2) / sin(theta1)

1 / 1.65 = sin(theta2) / sin(40)

theta2 = 22.93 degree

n / 1 = sin(90) / sin(22.93)

n = 2.567

in order to change the apparatus that would result in total internal reflection change the refractive index to 2.567

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