In a single slit diffraction experiment, a slit of width (0.016 ± 0.002) mm is used to measure the wavelength of a monochromatic light source. In the diffraction pattern, the angular distance between the central maximum and first minimum is measured to be (2° ± 40′). The value of the fractional error in the measurement of wavelength is: [Given: sin(2°) = 0.035]
Physics · Wave Optics · diffraction of light
JEE Advanced 2026 Paper 2

Question

In a single slit diffraction experiment, a slit of width (0.016 ± 0.002) mm is used to measure the wavelength of a monochromatic light source. In the diffraction pattern, the angular distance between the central maximum and first minimum is measured to be (2° ± 40′). The value of the fractional error in the measurement of wavelength is: [Given: sin(2°) = 0.035]

Physics · Wave Optics · diffraction of light

JEE Advanced 2026 Paper 2

G1 Physics · Accepted Answer

For the first minimum, λ = a sinθ. Hence fractional error approximately equals Δa/a + |cotθ|Δθ. Here Δa/a = 0.002/0.016 = 0.125. Also Δθ = 40′ = 2/3° ≈ 0.0116 rad, and cot2° ≈ cos2°/sin2° ≈ 1/0.035 ≈ 28.6. Thus the angular contribution is about 0.33. Total fractional error ≈ 0.125 + 0.33 ≈ 0.46.