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Q.

A concave lens of glass, refractive index 1.5, has both surfaces of the same radius of curvature R. On immersion in a medium of refractive index 1.75 it will behave as a

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a

convergent lens of focal length 3.5 R

b

convergent lens of focal length 3.0 R

c

divergent lens of focal length 3.5 R

d

divergent lens of focal length 3.0 R

answer is A.

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Detailed Solution

The focal length of a lens of refractive index surrounded by a medium of refractive index  μ1 is given
by

1f=μ2-μ1μ11R1-1R2
 

Hence, we have
-1f=1.5-1.751.751R+1R =-0.251.752R

which gives f = 3.5 R. Since the focal length is positive, the lens acts like a convergent lens.

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