In the figure, light enters a 90 degree triangular prism at point P with inciden

Question

In the figure, light enters a 90 degree triangular prism at point P with incident angle theta, and then some of it refracts at point Q with an angle of refraction of 90 degrees. (a) What is the index of refraction of the prism in terms of theta? (b) What, numerically, is the maximum value that the index of refraction can have? Does light emerge at Q if the incident angle at P is (c) increased slightly and (d) decreased slightly?

In the figure, light enters a 90 degree triangular prism at point P with incident angle theta, and then some of it refracts at point Q with an angle of refraction of 90 degrees. (a) What is the index of refraction of the prism in terms of theta? (b) What, numerically, is the maximum value that the index of refraction can have? Does light emerge at Q if the incident angle at P is (c) increased slightly and (d) decreased slightly?

Explanation / Answer

using snell's law:

sin(theta)/sin(theta/2) = n/1

where n=refractive index of prism

1=refractive index of air

now

as sin(theta)=2*sin(theta/2)*cos(theta/2)

we get

n=2*cos(theta/2)

b)now theta can be varied from 0 to 90 degrees.

so maximum will occur at theta=0

so maximum value of refractive index=2*cos(0/2)=2*1=2

c)at Q,

incident angle is theta/2

if refraction angle is alpha,

then sin(theta/2) / sin(alpha)= 1/n

alpha=theta

so it will emerge at Q,if alpha decreases or in turn if theta decreases.

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