One end of a horizontal cylindrical glass rod `(mu=1.5)` of radius 5.0 cm is rounded in the shape of a hemisphere. Asnobject 0.5 mm high is placed perpendicular to the axis of the rod at a difference of 20.0 cm 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.