A slit of width a is illuminated by monochromatic light of wavelength 650 mm at normal incidence calculate the value of a when
(a). The first minimum falls at an angle of diffraction of `30^(@)`
(b). The first maximum falls at an angle of diffraction of `30^(@)`.

Explanation

To solve the problem, we will use the principles of single-slit diffraction. The conditions for minima and maxima in single-slit diffraction are given by the following equations:

1. For the first minimum:
\[ a \sin \theta = m \lambda \]
where \( m = 1 \) for the first minimum, \( a \) is the slit width, \( \theta \) is the angle of diffraction, and \( \lambda \) is the wavelength.

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