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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°:

1. the absolute error in d remains constant
2. the absolute error in d increases
3. the fractional error in d remains constant
4. the fractional error in d decreases

Correct answer: the fractional error in d decreases

Solution

As θ increases, the value of sin θ approaches 1, reducing the relative impact of errors in θ on d. This causes the fractional error in d to decrease, even though the absolute error may vary.

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