Question

For the given incident ray as shown in figure, for total internal refraction of this ray the minimum refractive index of prism will be-

Answer 1

we know that for TIR ANGLE OF INCIDENCE SHALL BE  more than critical angle, ie, Θ>c

see diagram, ∠r + ∠ Θ =90°

sini/sinr  =μ  

,ie sin 45/ sin r= μ

sinr= 1/ μ√2

Θ> c,  ie, sinΘ> sin c

sin90-r > 1/μ

cosr >1/μ

√1-sin^2(r)  >1/μ

1- 1/2μ^2  > 1/μ^2

1 > 1/2μ^2  + 1/μ^2

μ^2  > 3/2

μ= √3/√2

its easy try writing on notebook u will understand this better then.

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