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Wave Optics

Question
CBSEENPH12039164

A ray of light passes through an equilateral glass prism such that the angle of incidence is equal to the angle of emergence and each of these angles is equal to 3/4 of angle of prism. Find the angle of deviation.

                                                              OR 

Calculate the speed of light in a medium whose critical angle is 45°. Does critical angle for a given pair of media depend on the wavelength of incident light? Give reason.          

Solution

Given, i = e = ¾ A,                              …(1)

where,
A is the angle of prism.

Angle of deviation for a ray of light in a prism is given by,
straight delta space equals space straight i space plus space straight e space minus space straight A

Since space straight e space equals space straight i. space we space have

straight delta space equals space 2 straight i space minus space straight A

Therefore space from space eqn. space left parenthesis 1 space right parenthesis comma space we space have space

space space space space straight delta space equals space 2 space straight x space 3 over 4 space straight A space minus space straight A
rightwards double arrow space straight delta space equals space 1 half straight A
Prism is an equilateral triangle. 
That is A= 60o
rightwards double arrow space delta space equals space 1 half cross times 60 space equals space 30 degree space semicolon space is space the space required space
angle space of space minimum space deviation. space


                                                          OR

Using the snell's law we have
mu space equals space fraction numerator 1 over denominator sin space C end fraction                                       ... (1)
where, C is the critical angle of the medium and straight mu is the refractive index of  the medium.
Also, mu space equals space c over nu                                     ... (2)

Now, from equations (1) and (2), we have 
straight c over straight nu equals straight space fraction numerator 1 over denominator sin straight space straight C end fraction
Error converting from MathML to accessible text.
This is the speed of the light in the medium. 
Refractive index of a medium is inversely proportional to the wavelength of light. So, critical angle also depends upon the wavelength of incident light.

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