A glass prism of refractive index 1.5 is immersed in water (refractive index `4//3`) . A light beam normally on the face AB is totally reflected to reach on the face BC if

Options

A. `sinthetage(8)/(9)`
B. `(2)/(3) lt sintheta ge lt (8)/(9)`
C. `sintheta le (2)/(3)`
D. `sintheta le (8)/(9)`

Answer

a.

Explanation

The phenomenon of total internal reflection takes place during reflection at P.
`sintheta=(1)/(._(g)^(w)mu)` (i)
where `theta` is the angle of incidence at P.
Now, `._(g)^(w)mu=(._(g)^(a)h)/(._(g)^(a)mu)=(1.5)/(4//3)=1.125`
Putting in (i),
` sintheta=(1)/(1.125)=(8)/(9)`
Therefore, `sintheta` should be greater than `(8)/(9)`