Question: Which of the following statements is incorrect?

Step 1 (Governing Law & Definition): [0.25 Mark]
The linear magnification $m$ for spherical mirrors and thin lenses is defined as the ratio of the height of the image ($h_i$) to the height of the object ($h_o$): $$m = \frac{h_i}{h_o}$$ According to the Cartesian sign convention, $h_o$ is always taken as positive (upward). Therefore, the sign of $m$ depends on the orientation of the image.

Step 2 (Step-by-Step Analysis): [0.50 Mark]
Let us evaluate each statement based on optical principles:

• (A) For a convex mirror, magnification is always negative: A convex mirror always forms a virtual, erect, and diminished image. For an erect image, $h_i$ is positive, so $m = \frac{+h_i}{+h_o} = +ve$. Thus, this statement is incorrect.
• (B) For all virtual images formed by a mirror, magnification is positive: Virtual images are always erect. Since $h_i$ and $h_o$ are both positive, $m$ is positive. This statement is correct.
• (C) For a concave lens, magnification is always positive: A concave lens always forms a virtual, erect, and diminished image. Since the image is erect, $m$ is positive. This statement is correct.
• (D) For real and inverted images, magnification is always negative: Real images are inverted ($h_i$ is negative). Thus, $m = \frac{-h_i}{+h_o} = -ve$. This statement is correct.

Step 3 (Final Concluded Answer): [0.25 Mark]
Since statement (A) claims magnification is negative for a convex mirror (which is physically impossible as it only forms erect images), the incorrect statement is (A).

💡 EL10 Concept Insight: Think of magnification like a mirror's "orientation check": if the image is standing upright (erect), the magnification is positive, and if it's flipped upside down (inverted), it's negative. Because a convex mirror always keeps the image standing upright, its magnification can never be negative!