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A concave lens of glass, refractive inde...

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

A

concave lens of focal length 1.75 R

B

concave lens of focal length 3.5 R

C

convex lens of focal length 2.5 R

D

convex lens of focal length 3.5 R

Text Solution

Verified by Experts

The correct Answer is:
D
For the concave lens, `R_(1)` is -ve and `R_(2)` is +ve
and `R_(1)=R_(2)=R`
`therefore (1)/(f) = -(n-1)((1)/(R )+(1)/(R ))= -[(2(n-1))/(R )]`
When it is dipped in the liquid, we consider
`" "_(L)n_(g)=(n_(g))/(n_(L))=(1.5)/(1.75)`
`therefore (1)/(f_(L)) = -(2)/(R ) ((1.5)/(1.75)-1)= -(2)/(R )[-(0.25)/(1.75)]`
`=(2)/(R )xx(1)/(7 )=(2)/(7R)`
`therefore f_(L) =(7R)/(2)=3.5 R`
`therefore` It acts like a convex lens of focal length 3.5 R.
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