Using the expression 2dsinθ=λ, one calculates the values of d by measuring the corresponding angles θ in the range 00 to 900. The wavelength λ is exactly known and the error in θ is constant for all values of θ. As θ increases from 100.
A
the absolute error in d remains constant.
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B
the absolute error in d increases.
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C
the fractional error in d remains constant.
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D
the fractional error in d decreases.
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Solution
The correct option is D the fractional error in d decreases. 2dsinθ=λ
⇒d=d2sinθ
Taking log and differentiating both sides-
Δdd=Δλλ−1sinθcosθΔθ
For maximum possible error all the errors should be added
⇒Δdd=Δλλ+cosθsinθΔθ
As λ is exactly known, Δλ=0
⇒Δdd=cotθΔθ
As Δθ1 is constant and on increasing θ,cotθ decreasees. So, fractional error in d(i.eΔdd) will also decrease.