A glass sphere of radius `R=10cm` is kept inside water. A ponit 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 starting 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)/10orAI_(1)=-30 cm`
Now, the first image `I_(1)`, acts as an object for the second surface, where
`BI_(1)=u=-(30+20)=-50 cm`
`therefore` `(4//3)/(BI_(2))-(3//2)/(-50)=(4//3-3//2)/(-10)`
`thereforeBI_(2)=-100 cm` i.e, the final image `I_(2)` is virtual and is formed at a distance 100 cm (towards left) from B. The ray diagram as shown.

Following points should be noted while drawing the ray diagram.
(i) At P the ray travels from rare to a denser medium. Hence, it will bend towards normal PC. At M, it travels from a denser to a rarer medium, hence, 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)`.