In an experiment for estimating the focal length of a converging mirror, image of an object placed at 40 cm from the pole is formed at distance 120 cm from the pole. These distances are measured with a scale having 20 small divisions in 1 cm. The error in measurement of focal length is 1/K cm. The value of K is ______.
Physics · Circular Motion
JEE Mains 30 January 2023 Shift 1 Morning Shift

Question

In an experiment for estimating the focal length of a converging mirror, image of an object placed at 40 cm from the pole is formed at distance 120 cm from the pole. These distances are measured with a scale having 20 small divisions in 1 cm. The error in measurement of focal length is 1/K cm. The value of K is ______.

Physics · Circular Motion

JEE Mains 30 January 2023 Shift 1 Morning Shift

G1 Physics · Accepted Answer

Mirror formula gives 1/f = 1/v + 1/u with u = −40 cm and v = −120 cm, giving f = −30 cm. Least count is 1/20 cm. Error propagation: |df|/f² = |du|/u² + |dv|/v² = (1/20)(1/40² + 1/120²). This gives |df| = 1/32 cm. Hence K = 32.