When a pin is moved along the principal axis of a small concave mirror, the image position coincides with the object at a point `0.5m` from the mirror. If the mirror is placed at a depth of `0.2m` in a transparent liquid, the same phenomenon occurs when the pin is placed `0.4m` from the mirror. find the refractive index of the liquid shown in fig.

Options

A. `6//5`
B. `5//4`
C. `4//3`
D. `3//2`

Answer

D

Explanation

Image position coincides with the object when an object is placed on centre of curvature i.e. R= 0.5m when transparent liquid is filled then phenomenon occurs when the pin placed 0.4 m from mirror i.e. effective distance must be 0.5 again
`0.2 + mu 0.2 = 0.5` , `mu= 3//2`