HC Verma Chapter 18 Problem 55 – Glass ball as lens – image of object on surface

Given

Glass ball diameter 10 cm (R=5 cm), n=1.5, object on surface

Find

Image by two refractions

Formula

First surface sends rays to infinity; second surface focuses parallel rays

Solution

First surface: u=0, image at infinity. Second surface R=-5: 1/v = (n2-n1)/(n1 R2) = (1-1.5)/(1.5 x (-5)) = 0.1; v = 10 cm beyond second surface

Answer

Image 10 cm beyond ball surface

Diagram / Concept

First surface collimates; second surface focuses

Notes

Solid glass sphere is a converging lens element