On an optical bench of 150 cm, a student used a concave mirror of focal length 20 cm to observe object distance (u) and image distance (v) respectively as:
(A) (40 cm, 10 cm)
(B) (60 cm, 15 cm)
(C) (80 cm, 38 cm)
(D) (60 cm, 30 cm)
(E) (40 cm, 40 cm)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (D) and (E) only
A pair of readings is consistent with a concave mirror of \( f = 20\,\mathrm{cm} \) if it satisfies the mirror formula. For a real object and real image, both in front of the mirror, the formula in magnitudes (cm) is \( \frac{1}{u}+\frac{1}{v} = \frac{1}{f} = \frac{1}{20} \).
(A) (40 cm, 10 cm) — Does not fit. \( \frac{1}{40}+\frac{1}{10} = \frac{1}{8} \), which gives \( f = 8\,\mathrm{cm} \).
(B) (60 cm, 15 cm) — Does not fit. \( \frac{1}{60}+\frac{1}{15} = \frac{1}{12} \), which gives \( f = 12\,\mathrm{cm} \).
(C) (80 cm, 38 cm) — Does not fit. \( \frac{1}{80}+\frac{1}{38} = \frac{118}{3040} \), which gives \( f \approx 25.8\,\mathrm{cm} \).
(D) (60 cm, 30 cm) — Fits. \( \frac{1}{60}+\frac{1}{30} = \frac{3}{60} = \frac{1}{20} \), so \( f = 20\,\mathrm{cm} \).
(E) (40 cm, 40 cm) — Fits. \( \frac{1}{40}+\frac{1}{40} = \frac{1}{20} \), so \( f = 20\,\mathrm{cm} \).