One face of prism of refracting angle `30^@` and refractive index `1.414` is silvered. At what angle must a ray of light fall on the unsilvered face so that it retraces its path out of the prism ?

Answer

`45^(@)`

Explanation

Here, `A = 30^(@), mu = 1.414, i_(1) = ?`
The ray will retrace its path when it falls normally on silvered face `AC` of the prism, Fig.

i.e., `i_(2) = 0, r_(2) = 0`
As `r_(1) + r_(2) = A`
`r_(1) = 30^(@)`
As `mu = (sin i_(1))/(sin r_(1))`
`:. sin i_(1) = mu sin r_(1) = 1.414 sin 30^(@)`
`= (sqrt(2))/(2) = (1)/(sqrt(2))`
`:. i_(1) = 45^(@)`