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Question:

A converging beam of light travelling in air converges at a point P as shown in the figure. When a glass sphere of refractive index 1.5 is introduced in between the path of the beam, calculate the position of the image. Also draw the ray diagram for the image formed.

Solution:

Here u=20cm, R=5cm, For 1st refraction 1.5/v - 1/20 = (1.5-1)/5
3/2v - 1/20 = 1/10
3/2v = 1/10 + 1/20 = 3/20
2v = 20
v = 10cm
For 2nd refraction u=0, v=0
1/v - 1.5/u = (1-1.5)/(-5)
So final image will be at pole of surface 2.