Question

A convex lens of focal length 20 cm produces image of size twice as that of the object kept at two distances x,
$x_1$ and $x_2$ ($x_1>x_2)$ from the lens. The ratio of $x_1$ and $x_2$

• A. 5 : 3
• B. 2 : 1
• C. 4 : 3
• D. 3 : 1

Answer 1

The correct option is D 3 : 1

Since, image formed by a convex lens can be real or virtual in nature.
Thus, m = + 2 or - 2.
First,
let us make image to be real in nature,
then
$m=-2=\frac{v}{u},$ where v is image distance and u is object distance.

$\Rightarrow v=-2x_1[Takingu=x_1]$

Now, by using lens equation,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\Rightarrow \frac{1}{-2x_1}-\frac{1}{x_1}=\frac{1}{20}\Rightarrow \frac{-3}{2x_1}=\frac{1}{20}$

$\Rightarrow x_1=-30cm$
Now, let us take image to be virtual in nature, then

$m=2=\frac{v}{u}\Rightarrow v=2x_2[Takingu=x_2]$

Again, by using lens equation,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{1}{2x_2}-\frac{1}{x_2}=\frac{1}{20}$

$\Rightarrow -\frac{1}{2x_2}=\frac{1}{20}$

$\Rightarrow x_2=-10cm$

So, the ratio of $x_{1}and{x}_2$

$\frac{x_1}{x_2}=\frac{-30}{-10}=3:1$