A thin equiconvex lens of refractive index `3//2` is placed on a horizontal plane mirror as shown in figure. The space between the lens and the mirror is filled with a liquid of refractive index `4//3` . It is found that when a point object is placed 15 cm above the lens on its priincipal axis, the object coincides with its own image.

Q. The radius of curvature of the convex surface is

Options

A. 10cm
B. 15cm
C. 20cm
D. 25cm

Answer

a

Explanation

The light retraced its path if it is incident normally on a mirror. The ray after refraction through the lens and the liquid are parallel. We will apply the general thin lens equation with parameters.
`n_(1)=1, n_(2)=3//2, n_(3)=4//3, u=-15cm, and upsilon=oo`
`(n_(3))/(upsilon)-(n_(1))/(u)=((n_(2)-n_(1)))/(R)+((n_(3)-n_(2))/(R))`
`(n_(3))/(oo)-(1)/((-15)) =((3//2)-1)/(R)-([(4//3)-(3//2)])/(R)`
On solving for R, we get `R=10cm`. Similarly, when second liquid is filled, we have
`(n_(3)^('))/(oo)-(1)/((-25))=((3//2)-1)/(10)-(n_(3)^(')-(3//2))/(10)`
On solving for `n_(3)^(')` , we get, `n_(3)^(')=1.6`