Ray Optics: Common Mistakes and Fixes (7)

For a concave mirror with object on the left:

• Object distance $u = -30 \text{ cm}$ (object is on the incident side)
• Focal length $f = -20 \text{ cm}$ (concave mirror, focus on the same side as the object)

The mirror formula:

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$

$\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{-20} - \frac{1}{-30} = -\frac{1}{20} + \frac{1}{30}$

Common denominator $60$:

$\frac{1}{v} = -\frac{3}{60} + \frac{2}{60} = -\frac{1}{60}$

$v = -60 \text{ cm}$

The negative sign tells us the image is on the same side as the object — a real image.

$m = -\frac{v}{u} = -\frac{-60}{-30} = -2$

Magnification of $-2$: image is twice as tall, inverted (negative sign), and real (we already saw $v < 0$).

Mistake A: Student uses $f = +20 \text{ cm}$ (treats focal length as always positive). Result: $v = +60 \text{ cm}$, virtual image — wrong nature entirely.

Mistake B: Student writes $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ (wrong sign in the formula — confusing it with the lens-maker convention). Gets nonsense.

Mistake C: Student computes $m = +v/u$ (drops the minus sign in the magnification formula for mirrors). Gets $m = +2$ instead of $-2$, calls the image erect — wrong.