Two cancave refracting surfacwe of equal radii fo curvature face each other in air as shown in figure. A point object O is placed midway between the centre and one of the poles. Then the separation between the images of O formed by each refracting surface is

Options

A. `11.4` R
B. `1.14` R
C. `0.114R`
D. `0.0114R`

Answer

C

Explanation

`I_(1)` due to refraction at surface (1)
`(1.5)/(V)-(1)/(R//2)=(1.5-1)/(R)`
`(1.5)/(V)=(2)/(R)+(0.5)/(R)`
`(1.5)/(V)=(2.5)/(R)`
`V=(15)/(R)`
`rArr(3)/(5)R=0.6R`
`I_(2)` due to refraction at surface (2)
`(1.5)/(V)=(2)/(-3R//2)-(1.5-1)/(-R)`
`(1.5)/(V)=-(2)/(3R)-(0.5)/(R)`
`(1.5)/(V)=(-3.5)/(3R)`
`V=(+4.5)/(3.5)R`
`rArr-(9)/(7)R`
`rArr-1.285R`

distance between `I_(1)&I_(2)=0.114R`