In an experiment to measure the focal length of concave mirror it was found that for an object distnace of 0.30 m, the image distance come out to be 0.60 m. Determine focal length with error limits.

Case 1: If we take vernier callipers, its least count  is : dv = du = 0.01cm = 10^-4m

Case 2: If we take meter scale, its least count  is : dv = du = 0.1cm = 10^-3m

v-image distance

u-object distance

f-focal length

then 1/v + 1/u = 1/f

for v=0.6m and u=0.3m , we have (from above formula) f = 0.2m

on differentiating above eqn. for error analysis, we have

 -dv/v² -du/u² =  -df/f²

Case 1(vernier scale):  df = f²( dv/v² +du/u² )

                                                = 0.04*(1/0.36 + 1/0.09)*10^-4m

                                                = 5.56x10^-5 m

                                    focal length limits are : ( 0.2 ± 5.56x10^-5 ) mts

Case 2(metee scale):  df = f²( dv/v² +du/u² )

                                              = 0.04*(1/0.36 + 1/0.09)*10^-3m

                                              = 5.56x10^-4 m

                                      focal length limits are : ( 0.2 ± 5.56x10^-4 ) mts

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