A glass sphere of radius `R=10cm` is kept inside water. A point object O is placed at `20cm` from A as shown in figure. Find the position and nature of the image when seen from other side of the sphere. Also draw the ray diagram. Given, `mu_g=3//2` and `mu_w=4//3`

Explanation

A ray of light stating from O gets refracted twice. The ray of light is travelling in a
direction from left to right. Hence, the distances measured in this direction are taken positive.
Applying `mu_2/v-mu_1/u=(mu_2-mu_1)/R`, twice with proper signs. We have,
`(3//2)/(AI_1)-(4//3)/-20=(3//2-4//3)/10` or `AI_1=-30cm`
Now, the first image `I_1` acts as an object for the second surface, where
`BI_1 = u = - (30+20)=-50cm`
`(4//3)/(BI_(2)) - (3//2)/(-50) = (4//3-3//2)/(-10)`

`:. BI_2 =-100cm`
i.e. the final image `I_2` is formed at a distance 100cm (towards left) from B.
The ray diagram is as shown in Fig. `31.32`
Following points should be noted while drawing the ray diagram.
(i) At P the ray travels from rarer to a denser medium. Hence, it will bend towards normal PC.
At M, it travels from a denser to a rarer medium, hence, it moves away from the normal MC.
(ii) PM ray when extended backwards meets at `I_1` and MN ray when extended meets at `I_2`.