Using the expression 2d sin θ = λ, one calculates the values of d by measuring the corresponding angles θ in the range 0 to 90°. The wavelength λ is exactly known and the error in θ is constant for all values of θ. As θ increases from 0° :-
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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 90°. The wavelength λ is exactly known and the error in θ is constant for all values of θ. As θ increases from 0° :-

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G1 Physics · Accepted Answer

From 2d sinθ=λ, d=λ/(2sinθ). With λ exact, |Δd|/d = |cotθ|Δθ for small constant Δθ. Since cotθ decreases as θ increases from 0° to 90°, the fractional error decreases. Correct answer: D.