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: (2^ ) = 0.035]
A. A
For a single slit diffraction, the condition for the first minimum is given by: a = Taking the natural logarithm on both sides, we get: = a + ( ) Differentiating to find the maximum fractional error: = a a + Since = 2^ is very small, 1, which gives 1 . Given (2^ ) = 0.035, we can approximate the angle in radians as = 0.035 rad. The error in the angle is = 40' = ( 40 60 )^ = ( 2 3 )^ . Converting into radians: = 2 3 ( 0.035 2 ) = 0.035 3 rad The fractional error in the angular term is: = 0.035 3 0.035 = 1 3 The fractional error in the slit width is: a a = 0.002 0.016 = 1 8 Substituting these values into the error equation: = 1 8 + 1 3 = 3 + 8 24 = 11 24 Answer: 0.46
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