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`

Options

A. 200cm, virtual
B. 100cm, real
C. 100cm, virtual
D. 300cm , virtual

Answer

C

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)/(v)-(4//3)/(-20)=(3//2=4//3)/(10)`
or, `v=-30cm`
Now, the first image `I_(1)` acts as an object for the second surface, where
`BI_(1)=u=-(30+20)=-50cm`
`(4//3)/(v^('))-(3//2)/(-50)=(4//3-3//2)/(-10)`
Therefore, `v^(')=-100cm` i.e., the final image `I_(3)` is virtual and is formed at a distance of 100cm (toward left) from B. the ray diagram is as shown in figure.
Following points should be noted while drawing the rays diagram.
i. At P, the ray travels from a rarer to a denser medium. Hence, it will bend toward normal MC.
ii. PM ray when extended backward meets at `I_(1)` and MN ray when extended meets at `I_(2)`.