First slide

The lens

Question

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

Moderate

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

Solution

$\frac{f_{l}}{f_{a}} = \frac{{aμ}_{g} - 1}{_{a} μ_{g} - 1} = \frac{1 .5 - 1}{\frac{1 .5}{1.75} - 1} = - \frac{1 .75 \times 0 .50}{0 .25} = - 3 .5$
$∴ f_{l} = - 3 .5 f_{a} \Rightarrow f_{l} = + 3 .5 R (∵ f_{a} = R)$
Hence on immersing the lens in the liquid, it behaves as a converging lens of focal length 3.5 R.

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