A small object is enclosed in a transparent solid sphere of radius 8 cm. the object is situated at 2 cm from the centre of the sphere. If its image appears to be at 3.2 cm from the nearest side, then the refractive index of the material of the sphere is

Options

A. `1 . 62`
B. `1 . 45`
C. `1 . 55`
D. `1 . 50`

Answer

D

Explanation

According to question,
If `mu_(1) and mu_(2)` are refractive indices of first and second medium with respect to air, then
`(mu_(2))/(v)-(mu_(2))/(u) = ((mu_(2) -mu_(1))/(R))`
Given, refracting index of material of sphere, `mu_(1) = m` , refractive index of air , `mu_(2) = 1` , radius of sphere , R = 8 cm , u = - 6 cm,
v = - 3.2 cm
`rArr (1)/(-3.2)-(mu)/(-6)=(1-mu)/(8)`
`rArr (mu)/(6) - (1)/(3.2) = (1-mu)/(8)`
`rArr (mu)/(6) +(mu)/(8) =(1)/(8) +(10)/(32)`
`rArr (7mu)/(24) =(14)/(32)`
`rArr mu = 1.50`