A narrow parallel beam of light is incident on a transparent sphere of refractive index `n` if the beam finally gets focused at a point situated at a distance=`2xx("radius of sphere")` form the center of the sphere then find `n`?

Answer

`(4)/(3)`

Explanation

From (1) surface : `(n)/(v) - (1)/(oo) = (n-1)/(R), v = (nR)/(n-1)`
`implies (1)/(R) - (n)/(v-2R) = (1-n)/(-R), (2)/(R)=(n)/(R) + (n)/(v-2R)`
`(2)/(R) = (n(v-2R+R))/(R(v-2R)) implies 2v - 4R = nv -nR`
On putting the value of v
`2(nR)/(n-1) - 4R = (nxxnR)/((n-1)) = -nR`
2nR - 4nR + 4R = `n^(2)R - n^(2)R + nR, n=(4)/(3)`