Question

A $5.0$ diopter lens forms a virtual image which is $4$ times the object placed perpendicularly on the principal axis of the lens. Find the distance of the object from the lens.

• A. $15\text{cm}$
• B. $15\text{cm}$
• C. $25\text{cm}$
• D. $30\text{cm}$

Answer 1

The correct option is A $15\text{cm}$

Given, $P=5$ diopter (convex lens)
$\Rightarrow f=\frac{1}{5}\text{m}=20\text{cm}$
Since, a virtual image is formed, u and v both are negative.
Given, $\frac{v}{u}=4$
$\Rightarrow v=4u$ ...(1)
From lens formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{f}=\frac{1}{4u}-\frac{1}{u}\Rightarrow \frac{1}{20}=\frac{1-4}{4u}=-\frac{3}{4u}$
$\Rightarrow u=-15\text{cm}$
$\therefore$ object is placed $15\text{cm}$ away from the lens.

Why this question? Tip: A virtual and enlarged image is formed in a convex lens only- so f is positive.