Figure shows a transparent hemisphere of radius 3.0cm made of a material of refractive index 2.0.
- A narrow beam of parallel rays is incident on the hemisphere as shown in the figure. Are the rays totally reflected at the plane surface?
- Find the image formed by the refraction at the first surface.
- Find the image formed by the reflection or by the refraction at the plane surface.
- Trace qualitatively the final rays as they come out of the hemisphere.
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Given, $\mu_2=2.0$
So, critical angle $=\sin^{-1}\Big(\frac{1}{\mu_2}\Big)=\sin^{-1}\Big(\frac{1}{2}\Big)=30^{\circ}$
- As angle of incidence is greater than the critical angle, the rays are totally reflected internally.
- Here, $\frac{\mu_2}{\text{v}}-\frac{\mu_1}{\text{u}}=\frac{\mu_2-\mu_1}{\text{R}}$
$\Rightarrow \ \frac{2}{\text{v}}=\frac{1}{3}\Rightarrow \text{v}=6\text{cm}$
$\Rightarrow$ If the sphere is completed, image is formed diametrically opposite of A.
- Image is formed at the mirror in front of A by internal reflection.
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