An equi-convex lens, having radius of curvature 33 cm is placed on a horizontal plane mirror and a pin held 20 cm above the lens coincides with its image. Now the space between the and the mirror is filled with a liquid in order to coicide with the image the pin has to be raised by 5 cm. The refractive index of the liquid is

Options

A. 1.33
B. 1.53
C. 2.33
D. 2.66

Answer

A

Explanation

Since object and image coincide i.e., after refraction from lens rays are incident normally on mirror i.e., after refraction rays become parallel to principal axis i.e., they are coming from focus of convex lens i.e., focal length of convex lens `f_1=20cm`
Now combined focal length is 25 cm.
Let `f_2:` focal length of liquid lens
`(1)/(F)=(1)/(f_1)+(1)/(f_2)implies(1)/(25)=(1)/(20)+(1)/(f_2)`
`(1)/(f_2)=(1)/(25)-(1)/(20)=(-1)/(100)`
`(1)/(f_2)=(mu-1)((1)/(-R)-(1)/(infty))`
`(-1)/(100)=-(mu-1)/(33)impliesmu=1.33`