Which of the following forms a virtual and erect image for all positions of a real object?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Both (1) and (3)
Option (1) Concave lens — Incorrect. The statement is true. A concave lens gives a virtual and erect image of every real object. But this option names only one of the two such devices, so it is incomplete.
Option (2) Concave mirror — Incorrect. A concave mirror gives a virtual, erect image only when the object lies between its pole and its focus. For an object beyond the focus the reflected rays actually meet in front of the mirror, so the image is real and inverted.
Option (3) Convex mirror — Incorrect. The statement is true. A convex mirror gives a virtual and erect image of every real object. But this option names only one of the two such devices, so it is incomplete.
Option (4) Both (1) and (3) — Correct. With the Cartesian sign convention, a real object has \( u\lt0 \). Both statements hold for every such \( u \).
For a concave lens, \( f\lt0 \), so in \( 1/v=1/f+1/u \) both terms are negative. Hence \( v\lt0 \) always. The image is on the same side as the object, so it is virtual. Also \( m=v/u \) is positive, so it is erect, and (1) holds.
For a convex mirror, \( f\gt0 \), so in \( 1/v=1/f-1/u \) both terms are positive. Hence \( v\gt0 \) always. The image is behind the mirror, so it is virtual. Also \( m=-v/u \) is positive, so it is erect, and (3) holds.