Question

the refractive index of an equilateral prism is 1.3 what is the limiting angle of the incidence of a Ray that will be transmitted through the prism​

Answer 1

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We have a prism with a prism angle of 60o and refractive index 73−−√.

Let the angle of incidence, the first angle of refraction, the second angle of refraction and the angle of emergence be i,r1.r2 and e , respectively.

At the limiting angle of incidence for the ray to be transmitted through the prism, e=90o

⇒A=60o and e=90o.

In a prism, r1+r2=A⇒r2=A−r1.

We have, sinisinr1=73−−√

⇒sinr1=37−−√sini.

⇒cosr1=1−37sin2i−−−−−−−−−√.