Physics Q39 – JEE-MAIN 2025

A finite size object is placed normal to the principal axis at a distance of

30 cm

from a convex mirror of focal length

30 cm

. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is :

Clue 1 of 3: Image Formation by Convex Mirror

First, determine the position of the image formed by the convex mirror using the mirror formula.

🧠 Full Solution Path

Step 1: Calculate the image position from the convex mirror✦ Active

The object distance for the convex mirror is $u = - 30 cm$ . The focal length of the convex mirror is $f = + 30 cm$ . Using the mirror formula $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ :

\frac{1}{30} = \frac{1}{v_{1}} + \frac{1}{- 30}

\frac{1}{v_{1}} = \frac{1}{30} + \frac{1}{30} = \frac{2}{30} = \frac{1}{15}

v_{1} = + 15 cm

This means the image $I_{1}$ formed by the convex mirror is virtual and located $15 cm$ behind the convex mirror.

Step 2: Determine the position of the plane mirror for coinciding images○ Expand

Let the convex mirror be at the origin ( $x = 0$ ). The object is at $x = - 30 cm$ . The image $I_{1}$ is at $x = + 15 cm$ . Let the plane mirror be placed at a distance $d$ from the convex mirror. We assume the plane mirror is placed to the left of the convex mirror, at position $x = - d$ . The object for the plane mirror is the original object at $x = - 30 cm$ . The distance of the object from the plane mirror is $u_{p} = | - 30 - (- d) | = | - 30 + d |$ . The image formed by the plane mirror ( $I_{P}$ ) must coincide with $I_{1}$ (at $x = + 15 cm$ ). The image $I_{P}$ is formed at a distance $u_{p}$ behind the plane mirror. The position of $I_{P}$ is $- d + u_{p} = - d + | - 30 + d |$ . We need $- d + | - 30 + d | = 15$ . Since the object is at $- 30 cm$ and the plane mirror is at $- d$ , for the object to be in front of the plane mirror, $d$ must be less than $30 cm$ (i.e., $- 30 + d$ is negative). So, $| - 30 + d | = - (- 30 + d) = 30 - d$ . Substituting this into the equation:

- d + (30 - d) = 15

30 - 2 d = 15

2 d = 15

d = 7.5 cm

This value of $d = 7.5 cm$ is consistent with the assumption $d < 30 cm$ . Therefore, the distance between the two mirrors is $7.5 cm$ .

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Physics Question 39 – JEE-MAIN 2025

Clue 1 of 3: Image Formation by Convex Mirror

🧠 Full Solution Path