(a) Using Huygen's principle draw a diagram to whow propagation of a front originating from a monochrmatic source.
(b) Desctibe diffraction of light due to a single slit. Explain formation of a pattern of fringes obtained on the screen and plot showing variation of intensity with angle `theta` in single slit diffraction.

Explanation

(a) Depending on the shape of source of light wave-front can be of three types.
(i) Spherical wave front : When the source of light is a point source, the wave front ia a sphere with centre at the source an in fig. `1(a)`.

(ii) Cylindrical wave-front : When the source of light is linear, the wave-front is cylindrical as in fig. `1(b)`

(iii) Plane wave-front : When the linear source of light is at very large distance a small portion of cylindrical wave front appears to be palne as in fig. `1(c)`

(b) Diffraction of light at a single slit.
Figure shows the diffractions of a monochomatic wavefront from a single slit `(AB)`. The secondary wavelets that go straight across tha slit arrive at the lens in same phase and are brought of focus on the screen at `O.` Thus the intensity at `O` is maximum.

Consider now the rays making an angle `theta` with the direction of normal to the slit, such that a `sin theta=lambda`. In this case, if we imaging the slit to be divided into two equl parts `AC` and `CB`, then for every point in `AC,` there is point in `CB` such that the path difference between the rays from these points is `lambda//2.` Thus the points `P` and `P'` at which these rays converge will be minima. Since `theta` is very small this gives `theta=lambda//a.` Angular width of central maximum `=2theta=(2lambda)/(a).` The intensity distribution curve for diffraction at a single slit is shown below.