How would the diffraction pattern of a single slit be affected when: (i) the width of the slit is decreased? (ii) the monochromatic source of light is replaced by a source of white light ?

When considering the diffraction pattern of a single slit, two key factors influence the observed pattern: the width of the slit and the nature of the light source. Let’s analyze both cases in detail.

(i) Effect of decreasing the width of the slit:
The diffraction pattern of a single slit is governed by the equation for the angular width of the central maximum:

θ = λ / a

where:

θ is the angle subtended by the first minimum with respect to the central axis,
λ is the wavelength of the light,
a is the width of the slit.
When the width of the slit (a) is decreased, the value of θ increases, meaning that the central maximum becomes broader. This happens because a narrower slit allows the waves to spread out more due to diffraction. Additionally, the intensity of the central maximum decreases because less light is passing through the narrower slit. The positions of secondary maxima and minima also shift outward.

Thus, decreasing the slit width results in a wider and less intense central maximum, with all fringes spreading further apart.

(ii) Effect of replacing monochromatic light with white light:
Monochromatic light consists of a single wavelength, leading to a uniform diffraction pattern with a well-defined central maximum and evenly spaced secondary maxima and minima.

When white light, which consists of multiple wavelengths (ranging from violet to red), is used instead of monochromatic light, the diffraction pattern is modified in the following ways:

Colored Fringes: Different wavelengths of light diffract by different amounts because θ = λ / a implies that longer wavelengths (such as red) will spread out more than shorter wavelengths (such as violet). As a result, the central maximum remains white, but the fringes become colored due to dispersion.

Overlapping of Diffraction Patterns: Each wavelength component of white light produces its own diffraction pattern, which slightly overlaps with the others. This leads to a rainbow-like effect in the secondary fringes, where the inner edge of each fringe appears blue (shorter wavelength) and the outer edge appears red (longer wavelength).

Less Distinct Secondary Maxima: Since different wavelengths interfere differently, the sharpness of secondary fringes reduces, making them less distinct compared to monochromatic light.

In summary:

If the slit width is decreased, the central maximum becomes wider, and the intensity decreases.
If white light is used instead of monochromatic light, the diffraction pattern becomes colored, with overlapping fringes and reduced sharpness in secondary maxima.