In a convex-lens focal-length experiment, object distance is 10±0.1 cm and real-image distance is 20±0.2 cm. The percentage error in f is n%. Find n.
Physics · Unit dimension and error
JEE Advanced 2023

Question

In a convex-lens focal-length experiment, object distance is 10±0.1 cm and real-image distance is 20±0.2 cm. The percentage error in f is n%. Find n.

G1 Physics · Accepted Answer

f=uv/(u+v)=200/30=6.667 cm. Differentiating, Δf/f = [v/(u+v)](Δu/u)+[u/(u+v)](Δv/v). Both relative distance errors are 1%, so Δf/f=1%. Hence n=1.