O is a point object kept on the principal axis of a concave mirror M of radius of curvature 20cm. P is a prism of angle `1.8^@` . Light falling on the prism (at small angle of incidence) gets refracted through the prism and then falls on the mirror. Refractive index of the prism is `3//2` . Find the distance between the images formed by the concave mirror due to this light.

Answer

`(pi)/(20)cm`

Explanation

For thin prism `delta=(mu-1)alpha`
`=(1.5-1)1.8^(@)`
`=(0.5)1.8xx(pi)/(180)rad=(pi)/(200)rad`
`:.` Distance `OO_(1)=10xx(pi)/(200)=(pi)/(20)cm`
Similarly, distance `OO_(2)=(pi)/(20)cm`
`:. O_(1)O_(2)=(pi)/(10)cm`
For the mirror, `O_(1)` and `O_(2)` are two point objects, at a distance of 30cm.
Now, applying mirror formula
`(1)/(v)+(1)/(-30)=(1)/(-10)rArrv=-15cm`
Latent magnification is
`-(v)/(u)=((-15))/(-30)=-(1)/(2)`
`(-ve` sign indicates inverted image `)`
Therefore, if `O_(1)^(')` and `O_(2)^(')` are the images formed, then distance between them,
`O_(1)^(')O_(2)^(')=(1)/(2)O_(1)O_(2)=(1)/(2).(pi)/(10)=(pi)/(20)cm`