A 4 cm axial rod is centred 30 cm from a concave mirror of focal length 20 cm. Find the percentage by which the infinitesimal longitudinal estimate exceeds the exact image length. Give the answer to one decimal place.
Physics · Geometrical optics · spherical mirror
JEE Mains NEET

Question

A 4 cm axial rod is centred 30 cm from a concave mirror of focal length 20 cm. Find the percentage by which the infinitesimal longitudinal estimate exceeds the exact image length. Give the answer to one decimal place.

Physics · Geometrical optics · spherical mirror

G1 Physics · Accepted Answer

Exact length from ends 28 and 32 cm is 70−53.333=16.667 cm. At centre u=30, |m|=2, so infinitesimal estimate=4×4=16 cm. It is actually lower by 4%; therefore the requested 'exceeds' wording would be negative. Correct signed percentage=(16−16.667)/16.667×100≈−4.0%.