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Ray Optics And Optical Instruments

Question

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A symmetric double convex lens is cut in two equal parts by a plane perpendicular to the principal axis. If the power of the original lens is 4D, the power of a cut lens will be

2D

3D

4D

5D

Solution

A.

2D

Biconvex lens is cut perpendicularly to the principal axis, it will become plano-convex lens.
Focal length of biconvex lens

$\frac{1}{f} = (n - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}}) \frac{1}{f} = (n - 1) \frac{2}{R} (∵ R_{1} = R, R_{2} = - R)$

$\Rightarrow f = \frac{1}{2 (n - 1)} . . . . (i)$

For plano-convex lens

$\frac{1}{f_{1}} = (n - 1) (\frac{1}{R} - \frac{1}{\infty}) f_{1} = \frac{R}{(n - 1)} . . . . . (ii)$

Comparing Eqs. (i) and (ii), we see that focal length becomes double

As power of lens P ∝ $\frac{1}{focal length}$

Hence, power will become half.

New power = $\frac{4}{2}$

New power = 2D

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