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

Question

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 (A)  2D  (B)  3D  (C)  4D  (D)  5D

Tardigrade Admin · Accepted Answer

Biconvex lens is cut perpendicularly to the principal axis, it will become a 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{R}{2 ( n - 1 )} \dots (i)

For plano-convex lens

\frac{1}{f _{1}} = (n - 1) (\frac{1}{R} - \frac{1}{\infty})

f_{1} = \frac{R}{( n - 1 )} \dots (ii)

Comparing Eqs.

(i)

and

(ii)

, we see that focal length becomes double.
As power of lens

P \propto \frac{1}{focal length}

Hence, power will become half.
New power

= \frac{4}{2} = 2 D

Q. 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 $4 D$ , the power of a cut lens will be

$2 D$

$3 D$

$4 D$

$5 D$

Q. 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

Q. 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 $4 D$ , the power of a cut lens will be

$2 D$

$3 D$

$4 D$

$5 D$