Question 219 of 295

An object is placed on the principal axis of convex lens of focal length $10cm$ as shown. A plane mirror is placed on the other side of lens at a distance of $20cm$. The image produced by the plane mirror is $5cm$ inside the mirror. The distance of the object from the lens is ____ $cm$.

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Answer: 30

Given here: Focal length of convex lens, $f=10cm$
Now, as seen in figure, image from lens is formed at point ${I}_{1}$, whose location is $5cm$ from mirror. Thus, ${I}_{1}$ is at $15cm$ from lens.
Using lens equation, we have
$\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$
Putting the value,
$\dfrac{1}{15}-\dfrac{1}{-u}=\dfrac{1}{10}$
$\Rightarrow \dfrac{1}{u}=\dfrac{1}{10}-\dfrac{1}{15} \Rightarrow u=\dfrac{10\times 15}{10-15}$
Thus, object is placed at $30cm$ from lens.