Question

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 ___$cm$

Answer 1

Correct Answer: 30

The correct answer is 30.

 

$f=10cm$
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{1}{15}-\frac{1}{-u}=\frac{1}{10}$
$\Rightarrow \frac{1}{u}=\frac{1}{10}-\frac{1}{15}$
On solving we get value of $u$ as $30cm$.

Answer 2

The system can be analyzed by considering the light passing through the lens, reflecting off the mirror, and then passing back through the lens. We apply the lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] For the first pass through the lens: \[ \frac{1}{15} - \frac{1}{-u} = \frac{1}{10} \] \[ \Rightarrow \frac{1}{u} = \frac{1}{10} - \frac{1}{15} \] \[ u = -30 \, \text{cm} \quad (\text{The negative sign indicates that the object is on the same side as the incoming light}) \] To ensure the image formed by the mirror is 5 cm inside, we need to calculate the equivalent object distance after the reflection from the mirror, which results in a distance of 30 cm.