Problem 1: Concave Mirror — N1

Given: Object 30 cm in front of concave mirror, f = 20 cm. Find: Image position, magnification, nature.

Step 1 — Assign signs: u = −30 cm (object on left, always negative). f = −20 cm (concave mirror, f < 0).

Step 2 — Apply mirror formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ $\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{-20} - \frac{1}{-30} = -\frac{1}{20} + \frac{1}{30} = \frac{-3+2}{60} = -\frac{1}{60}$

Step 3 — Image distance: v = −60 cm. Negative → real image (in front of mirror).

Step 4 — Magnification: $m = -\frac{v}{u} = -\frac{(-60)}{(-30)} = -\frac{60}{30} = -2$

m = −2: negative → inverted; |m| = 2 > 1 → magnified (2×).

Answer: Real, inverted, magnified (2×), 60 cm in front of mirror.