A paraxial beam is incident on a glass (n=1.5) hemisphere of radius R=6 cm in air as shown. The distance of point convergence F from the plane surface of hemisphere is :-

Options

A. 12cm
B. 5.4 cm
C. 18 cm
D. 8 cm

Answer

D

Explanation

(i) For (i) ` (u_(2))/(v_(1)) - (1)/(oo) = (u_(2)-1)/(6)`
`v_(1) = (3)/(2) xx 6 xx2 = 18 "cm"`

For plane surface : `I_(1) rarr "object"`
`d_("apperent") = (n_(2))/(n_(1))xx d_("actual") = (n_(2))/(n_(1)) xx (18-R)`
`(1)/(3//2)xx(18-6) = 8 "cm"`