Question

A parallel beam of light is incident on a transparent hemisphere of $$ RI= \,2 $$ as shown in figure . $$ O $$ is the centre of hemisphere . The radius of the hemisphere is $$ R $$ . Give the answer of the question :
For the situation described above , mark out the correct statements(s) :

Answer 1

Correct option is D. Both (a) and (b) are correct
when angle of incident ray is greater than critical angle, ray gets reflected through surface, this is called internal reflection.

critical angle $$i_{cric}=sin^{-1}{\frac{1}{\mu}}$$ where $$\mu$$ is refractive index of denser medium.

Here angle of incident $$i=45^o$$ and $$\mu=2$$

$$i_{cric}=sin^{-1}{\frac{1}{2}}$$

$$i_{cric}=sin^{-1}{0.5}$$

$$i_{cric}=30^o$$ and incident angle $$i =45^o$$ which is greater than critical angle $$i_{cric}$$.

Internal reflection takes place for central ray at plane surface.

As we move down from central ray of beam, incident angle decreases and as we move up from central ray incident angle increases.

so more the incident angle more the chance of TIR.

so as we move up from the central ray chances of TIR at plane surface is more.