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  • In an Isosceles prism of angle 45o , it is found that when the angle of incidence is same as the prism angle, the emergent ray grazes the emergent surface. <img alt="" src

In an Isosceles prism of angle 45o , it is found that when the angle of incidence is same as the prism angle, the emergent ray grazes the emergent surface.

The refractive index of material of the prism is:

Option: 1

\sqrt{2}

 

 


Option: 2

\sqrt{3}


Option: 3

4


Option: 4

\sqrt{5}


Answers (1)

 As the ray of light grazes the second surface r2 is the critical angle

\sin r_{2}=\frac{1}{\mu }

and we know 

r_{1 }+r_{2}=45^{0}

for incident plane 

\sin r_{1}=\frac{\sin 45^{0}}{\mu}

\sin r_{1}=\frac{1}{\sqrt{2}\mu}

\sin r_{1}=\sin (45^{0}-r_2)=\frac{1}{\sqrt{2}}(\cos r_{2}-\sin r_{2})

\frac{1}{\sqrt{2}\mu }=\frac{1}{\sqrt{2}}\frac{\sqrt{\mu ^{2}-1}-1}{{\mu }}

1=\sqrt{\mu ^{2}-1}-1 or {\mu ^{2}-1}=4

\mu =\sqrt{5}

Posted by

Kshitij

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