CBSE Class 12-science Answered

• Diffraction at a single slit (Fraunhofer diffraction)

The phenomenon of bending of light round the sharp corners of an obstacle and spreading into the regions of the geometrical shadow is called diffraction.

• Expression For Fringe Width

Consider a parallel beam of light from a lens falling on a slit AB. As diffraction occurs, the pattern is focused on the screen XY with the help of lens L₂. We will obtain a diffraction pattern that is a central maximum at the centre O flanked by a number of dark and bright fringes called secondary maxima and minima.

Central Maximum ? Each point on the plane wave front AB sends out secondary wavelets in all directions. The waves from points equidistant from the centre C lying on the upper and lower half reach point O with zero path difference and hence, reinforce each other producing maximum intensity at point O.

• Positions and Widths of Secondary Maxima and Minima

Consider a point P on the screen at which wavelets travelling in a direction making angle ? with CO are brought to focus by the lens. The wavelets from points A and B will have a path difference equal to BN.

From the right-angled ?ANB, we have

BN = AB sin?

BN = a sin? …(i)

Suppose BN = ? and ? = ?₁

Then, the above equation gives

? = a sin ?₁

Such a point on the screen will be the position of first secondary minimum.

If BN = 2? and ?= ?₂, then

2? = a sin ?₂

Such a point on the screen will be the position of second secondary minimum.