A fly F is sitting on a glass slab A , 45 cm thick and of refractive index 3/2 . The slab covers the top of a container B containing water (Refrective index 4/3) upto a height of 20 cm . The bottom of container is closed by a concave mirror C of radius of curvature 40 cm . Locate the final image formed by all reflection assuming paraxial rays.

Answer

`(45)/(2)` cm below F

Explanation

`x=45((4)/(3)) xx (2)/(3)= 40 cm`
So total distance = 60 cm

f = -20 cm
`(1)/(v) +(1)/(u) = (1)/(f)`
`implies (1)/(v) + (1)/((-60)) = (1)/(-20)`
`implies (1)/(v) = (1)/(60) - (1)/(20)= (-40)/(60 xx 20) implies v = -30`
So image after reflection from mirror will be at d=30 cm. So 10 cm above 'A'
After refraction at A : It will be at `(10)/((4//3))(3//2) = (90)/(8) = (45)/(4)` cm
so distance from 'B' layer is `(45 - (45)/(4)) = 45 xx (3)/(4)`
So final image after refraction at 'A' will be at :
`45 xx (3)/(4) xx (2)/(3) = (45)/(2)` from 'A' surface