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