Question

the radius of curvature of a concave mirror, measured by a spherometer, is given by R= l^2/6h+h/2. the values of l and h are 4.0cm and 0.065 cm respectively, where l is measured by a meter scale and h by a spherometer. Find the percentage error in the measurement of R​

Answer 1

Answer:

Given, l=3cm,Δl=0.1cm,h=0.045cm,Δh=0.005cm 

Now, R=6hl2+2h

Take ln and differentiate (only be taken magnitude)

so, relative error , RΔR=2lΔl+hΔh+hΔh=230.1+20.0450.005=0.3