A tranparent sphere of radius 20cm and refractive index 1.6 is fixed in a hole of the partition separating the two media: A(refractive index ` n_(1)=1.2)` and B ( refractive index `n_(3)=1.7)`. A luminous point object is placed 120cm from the surface of the sphere iin medium A. it is viewed from D in medium B in a direction normal to the sphere. Find the position of the image formed by the rays, from point N.

Options

A. 304cm, left side of N
B. 175 cm, right side of N
C. 204 cm, right side of N
D. 220cm, left side of N

Answer

C

Explanation

We will have to consider two refractions: first at surface `S_(1)` and the second at surface `S_(1)`.
For refraction at surface `S_(1)`:
`(1.6)/(v_(1))-(1.2)/((-120))=((1.6-1.2))/(20), upsilon_(1)=+160cm`
The positive sign implies that first image is formed to the right fo `S_(1)`.
For refraction at surface `S_(2)`:
The first image is object for refraction at second surface,
`upsilon_(2)=+(160-40)cm`
`(1.7)/(upsilon)-(1.6)/(+(160-40))=(1.6-1.7)/((-20)),upsilon_(2)=+204cm`
The final image is formed at 204cm from vertex and on the right side.