A light ray is incident perpendicular to one face of a `90^@` prism and is totally internally reflected at the glass-air interface. If the angle of reflection is `45^@`, we conculde that for the refractive index n as

Options

A. `nlt (1)/(root_2)`
B. `ngt root_2`
C. `ngt (1)/(root_2)`
D. `nlt root_2`

Answer

B

Explanation

According to condition of total internal reflection,
i = C where i = incidence angle, C = critical angle
`therefore sini gt sinC`
`therefore sini gt 1/n` [`becausen=(1)/(sinC)]`
`thereforen gt (1)/(sini)`
`therefore n gt (1)/(sin45^@)" "[becausei=45^@]`
`therefore n gt sqrt2" "[becausesin45^@=(1)/(sqrt2)`