A convex mirror produces the magnification 1/3 and 1/4 when the objec…

The correct answer is Option (2) → Q is far from the mirror as compared to P

A convex mirror always forms a virtual, erect and diminished image, and the image becomes smaller as the object moves farther away. From the mirror formula, with the Cartesian sign convention (\( f \) positive for a convex mirror, \( u \) negative):

    \( \displaystyle m = \frac{f}{f - u} = \frac{f}{f + |u|} \)

    \( \displaystyle m = \frac{1}{3}: \quad f + |u_P| = 3f \;\Rightarrow\; |u_P| = 2f \)

    \( \displaystyle m = \frac{1}{4}: \quad f + |u_Q| = 4f \;\Rightarrow\; |u_Q| = 3f \)

So Q is at \( 3f \) and P at \( 2f \): the smaller magnification belongs to the farther point, Q.

Option (1) P is far from the mirror as compared to Q — Incorrect. P gives the larger image, so it is the nearer point, at \( 2f \).

Option (2) Q is far from the mirror as compared to P — Correct. Q gives the smaller image and lies farther away, at \( 3f \).

Option (3) P and Q both are coinciding — Incorrect. Different magnifications mean different object distances, so P and Q cannot coincide.

Option (4) Convex mirror produces the magnification always greater than 1 — Incorrect. A convex mirror always gives a diminished image, so its magnification is always less than 1.