Question

Height of the image of an principal axis produced by a convex lens is double the object height . If the focal length of the lens is $20cm$, then the image distance from lens is :

• A. $10cm$
• B. $20cm$
• C. $40cm$
• D. Both $\left(1\right)\&\left(2\right)$

Answer 1

The correct option is B $20cm$

Magnification of image is, $|m|=2$ as image size (h') is double the object size (h)

Thus, $m=\pm 2$

as for a less, $m=\frac{v}{u}$ (object distance = 'u' , image distance = 'v')

$\Rightarrow \frac{v}{u}=\pm 2$ $\Rightarrow v=2u$ or $v=-2u$

(i) case I : $v=2u\Rightarrow u=v/2$ then by lens formula,

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{1}{v}-\frac{2}{v}=\frac{1}{20}\Rightarrow v=-20cm$

(ii) case II : when $v=-2u\Rightarrow u=-v/2$, so

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{1}{v}+\frac{2}{v}=\frac{1}{20}\Rightarrow v=20/3cm$

$\therefore$ Image distance can be $20cm$ (if image is virtual) on can be $20/3cm$ (if image is real)