One end of a horizontal cylindrical glass rod `(mu=1.5)` of radius `5 cm` is rounded in the shape of a hemisphere. An object `0.5mm` high is placed perpendicular to the axis of the rod at a distance of `20.0cm` from the rounded edge. Locate the image of the object and find its height`

Answer

`30 cm ; 0.5 mm`

Explanation

Taking vertex as the origin, Fig.

`u = PO = - 20 cm`
`R = + 5 cm, mu_(1) = 1, mu_(2) = 1.5`
Refraction from rarer to denser medium
`-(mu_(1))/(u) + (mu_(2))/(v) = (mu_(2) - mu_(1))/(R )`, we get `v = 30 cm`.
Image is formed inside the rod at a distance of `30 cm` from the vertex.
Magnification, `m = (mu_(1) v)/(mu_(2) u) = (1 xx 30)/(1.5 xx (- 20)) = -1`
`:.` Image will be of same height `(0.5 mm)` as the object, but it will be inverted.