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

Question

TestHub · Accepted Answer

Given here: Focal length of convex lens, $f = 10 cm$

Now, as seen in figure, image from lens is formed at point $I_{1}$ , whose location is $5 cm$ from mirror. Thus, $I_{1}$ is at $15 cm$ from lens.

Using lens equation, we have

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

Putting the value,

$\frac{1}{15} - \frac{1}{- u} = \frac{1}{10}$

$\Rightarrow \frac{1}{u} = \frac{1}{10} - \frac{1}{15} \Rightarrow u = \frac{10 \times 15}{10 - 15}$

Thus, object is placed at $30 cm$ from lens.

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