Board-style MCQs and past-paper numericals in the BIEK / Sindh Board pattern. Tap an option to check yourself instantly. Solved questions are at the bottom.
Multiple-choice questions
Solved numericals (past papers)
Concave mirror — image position & magnification
Object 30 cm in front of a concave mirror, f = 10 cm.
1/q = 1/f − 1/p = 1/10 − 1/30 = 2/30 → q = 15 cm (real, inverted)
m = q/p = 15/30 = 0.5 — half the object's size
Snell's law — refractive index & speed in glass
i = 45°, r = 28°.
n = sin 45° / sin 28° = 0.707 / 0.469 = 1.51
v = c/n = (3 × 10⁸) / 1.51 = 1.99 × 10⁸ m/s
Critical angle of diamond & of water
sin C = 1/n.
diamond: sin C = 1/2.42 = 0.413 → C = 24.4° (tiny → light trapped → sparkle)
water: sin C = 1/1.33 = 0.752 → C = 48.8°; a 55° underwater ray cannot escape (TIR)
Apparent depth of a swimming pool
Real depth 2.0 m, n(water) = 1.33.
apparent depth = real / n = 2.0 / 1.33 = 1.5 m — the floor looks 0.5 m higher than it is.
Convex lens — image, magnification & power; myopia prescription
p = 30 cm, f = +20 cm.
1/q = 1/20 − 1/30 = 1/60 → q = 60 cm, real & inverted · m = 60/30 = 2
P = 1/f(m) = 1/0.20 = +5 D
Myopic far point 2.0 m → spectacle f = −2.0 m → P = −0.5 D (concave lens)