JEE Advanced | 2013Errors in measurementMedium
Question
Using the expression 2d sin θ = λ one calculates the values of d by measuring the corresponding angles θ in the range 0 to 90o. The wavelength λ is exactly known and the error in θ is constant for all values of θ. As θ increases from 0o :-
Options
A.the absolute error in d remains constant
B.the absolute error in d increases
C.the fractional error in d remains constant
D.the fractional error in d decreases
Solution
cosθ δθ θ{δθ = constant}as θ increases,
decreases so Absolute error |δ(d)| decreases
Also fractional error
fractional error
as θ increases, cotθ decreases
So fractional error decreases
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