Question

A ray of light is incident at an angle of `60^@` on the face of a prism having refracting angle `30^@.` The ray emerging out of the prism makes an angle `30^@` with the incident ray. Show that the emergent ray is perpendicular to the face through which it emerges and calculate the refractive index of the material of prism.

Answer 1

Fig.
Here, `i_1 = 60^@, A = 30^@, delta = 30^@, i_2 = ?`
As `i_1 + i_2 = A + delta`
`:. 60^@ + i_2 = 30^@ + 30^@ = 60^@`
`i_2 = 0`
Hence emergent ray is normal to the surface,
When `i_2 = 0, r_2 = 0`
As `A = r_1 + r_2`
`:. 30 = r_1 + 0` or `r_1 = 30^@`
Now `mu = (sin i_1)/(sin r_1)=(sin 60^@)/(sin 30^@) = (sqrt(3))/(2 xx 1//2) = sqrt(3)`.
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