Question

A student measure the height h of a convex mirror using spherometer. The legs of the spherometer are 4 cm apart and there are 10 divisions per cm on its linear scale and circular scale has 50 divisions. The student takes 2 as linear scale division and 40 as circular scale division. What is the radius of curvature of the convex mirror ?

• A. $9.06cm$
• B. $20.66cm$
• C. $5.66cm$
• D. $9.66cm$

Answer 1

The correct option is D $9.66cm$

Least count of the spherometer is $LC=$ pitch/number of circular divisions $=\frac{1/10}{50}=0.002cm$
The total reading for height is $h=MSR+(CSR\times LC)=(2\times 0.1)+(40\times 0.002)=0.28cm$
The formula for radius of curvature is $R=\frac{l^2}{6h}+\frac{h}{2}=\frac{4^2}{6\left(0.28\right)}+\frac{0.28}{2}=9.66cm$