A hollow equiconvex lens made of a very thin glass sheet has one of its curved surfaces silvered. It converges a parallel beam of light at a distance of 0.2 m infront of it. Where will it converge the same rays if filled with water, refractive index n w = 4/3?
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Sol. As glass is thin, we can ignore its refractive effects. The lens behaves as an air lens with a glass boundary.
= (1 – 1) 
= 0
If R is the radius of curvature of the curved surface,
= 
, f m = 
With air inside, the system will behave as a concave mirror of focal length R/2. For parallel incoming rays, from mirror equation we have
+ 
= 
, f m = – 0.2 m
Hence, R = – 2f m = 0.4 m
When water is filled in the lens,
= 
= 
D
Power of composite system,
= 
+ 
+ 
= 2 × 
+ 
= 
Hence, F = – 0.12 m = – 12 cm
For parallel rays we have
– 
= 
v = – 12 cm
The final image is formed at 12 cm infront of the lens.
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