Question

One end of a cylindrical glass rod shown in figure ends in a hemispherical surface of radius R = 20 mm. Let the same rod be immersed in water of index 1.33, the other quantities having the same values as before. Find the image distance.

• A. 120 mm
• B. -120 mm
• C. 180 mm
• D. -180 mm

Answer 1

The correct option is D -180 mm


$\frac{1.5}{v}-\frac{1.33}{-80}=\frac{1.5-1.33}{20},v=-180mm.$
The fact that v is negative means that the rays, after reflection by the surface are not converging but appear to diverge from a point 180 mm to the left of the vertex.
In this illustration, then the surface forms a virtual image 180 mm to the left of the vertex.