# Diffraction of Light at a Single Slit

Chapter-10|Wave Optics|NCERT 12th Physics:

Diffraction of Light at a Single Slit:

A parallel beam of light with a plane wavefront is made to fall on a single slit LN. As LN=a is of the order of wavelength of light, therefore diffraction occurs on passing through the slit.

The wavelets from the single wavefront reach the centre C on the screen in same phase and hence, interfere constructively to give central maximum (bright fringe).

The diffraction pattern obtained on the screen consists of a central bright band, having alternate dark and week bright band of decreasing intensity on both sides.

When there are more than one source of light, then we can establish the condition for secondary Maxima. The slit is divided into 2,4,6,…….  equal parts such that the corresponding wavelets from successive regions interfere with path difference of λ/2.

Therefore, for nth secondary Maxima, the slit can be divided into 2n equal parts.

We observe that p is a dark point, if path difference is λ,2λ,3λ,…….. So from λ= asinθ

[aSinθ= nλ],      n=1,2,3,…….

To establish the condition for secondary Maxima, the slit is divided into 3,5,7,……. equal parts such that corresponding wavelets from alternate regions interfere with Path difference λ/2.

Therefore, for nth secondary Maxima, the slit can be divided into (2n+1) equal parts.

We observe that p is a bright point, when path difference is 3λ/2,5λ/2,7λ/2,………

[aSinθ= (2n+1)λ/2],       n= 1,2,3, ……..

Graph for Diffraction Pattern:

Width of Central Maximum:

The width of Central Maximum is the distance between first secondary minimum on either side of the central bright fringe O.