Radius of curvature of a spherical surface is given by, 

                             

where,

l is average distance between the three fixed legs of spherometer, and 

h is the height of the central screw above the plane surface. 

Here, X =Aⁿ 

Let ∆A and ∆X be the absolute errors in A and X respectively.

Therefore the above equation with error can be written as


 

Multiplying both sides by 100, 

 

i.e. Maximum possible %age error in X = n (Maximum possible %age error in A)

Let X = AB
Let ∆A, ∆B and ∆X be the absolute errors in A, B and X respectively. Therefore the above equation with error can be written as

   



Since,  are small quantities, theefore the product  will be very small and hence can be neglected. Thus the above equation reduce to 


Maximum value of fractional error in X is 



Multiplying both sides by 100


i.e. Maximum possible %age error in X
= Maximum possibe %age error in A + MAximum possible %age error in B.