Question

An object is placed 50cm from surface of glass sphere of radius 10cm along the diameter where will the final image be form after refraction at both surface.

Answer 1

Given:

u = - 50cm

R = 10cm

u1 = 1

u2 = 1.5  ( μ of glass)

To Find:

Diameter of the final image

Solution:

Refraction at surface P1A

Virtual image at I1 where P1I1 = v1

Thus,  

- u1/v + u2/v = u2 - u1/R

= - 1/50 + 1.5/v1  

= 1.5 - 1/10  

= 1/20

3/2v1 = 1/20 - 1/50 = 3/100 , v1 = 50cm

Refraction at surface P2B

u = P2I1 = P1I1 - P1P2

= 50 - 20

= 30cm

Thus,  

- u2/u + ui/v = u1-u2/R

= - 1.5/30 + 1/v  

= 1 - 1.5/-10  

= 1/20

1/v = 1/20 + 3/60 = 1/10 , v = 10cm

Distance of final image will be =  

CI = CP2 + P21  

= 10 + 10  

= 20

Answer: The diameter will be 20cm