Figure (18-E12) shows a transparent hemisphere of radius 3.0 cm made of a material of refractive index 2.0.
(a) 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?
(b) Find the image formed by the refraction at the first surface.
(c) Find the image formed by the reflection or by the refraction at the plane surface.
(d) Trace qualitatively the final rays as they come out of the hemisphere.
Radius of the transparent hemisphere R = 3.0 cm
Refractive index of the material =
= 2.0
Critical angle= 
Therefore, Critical angle 
= 
= 
(a) The angle of incidence id greater than critical angle. So the rays will be totally reflected internally.
(b) Using lens equation:
⇒ 
⇒ 
⇒ 
If the sphere is complete, image will be formed diametrically opposite of A.
(c) Image is formed at the mirror in front of A by internal reflection.