A ray of light incident at an angle `theta` on a refracting face of a prism emerges from the other face normally. If the angle of the prism is `5^@` and the prism is made of a material of refractive index `1.5`, the angle of incidence is.

Options

A. `7.5^(@)`
B. `5^(@)`
C. `15^(@)`
D. `2.5^(@)`

Answer

A

Explanation

Here, `A = 5^(@), mu = 1.5, i_(1) = ?`
As they ray emerges from the other face of prism normally,
`i_(2) = 0^(@). :. r_(2) = 0^(@)`, Fig.
As `r_(1) + r_(2) = A`
`r_(1) = A - r_(2) = 5 - 0 = 5^(@)`
From `mu = (sin i_(1))/(sin r_(1)), sin i_(1) = mu sin r_(1) = 1.5 xx sin 5^(@)`
`= 1.5 xx 0.087 = 0.1305`
`i_(1) = sin^(-1) (0.1305) = 7.5^(@)`