Question

What do you mean by the diffraction of light? The light of wavelength \[5000A^\circ \] is falling normally on a slit of width $2 \times 10^{-5}$ meter. Find the angular width of central maxima in the diffraction pattern.

Answer 1

Hint: (i) Diffraction as suggested by the name itself that it is the slight bending of light as it passes around the edge of an object.
(ii) The diffraction pattern obtained on the screen consists of a central bright band, having alternate dark and bright bands of decreasing intensity on both sides.

Complete step by step answer:
Step 1: Diffraction of light is the phenomena of bending of light around the corner of an obstacle or aperture in the path of light and this light penetrates into the geometrical shadow of the obstacle. Thus, this light deviates from its linear path.
The amount of deviation or bending depends on the relative size of the wavelength of light to the size of the aperture or opening. If the opening is much larger as compared to the wavelength of light then the bending or deviation will be almost unnoticeable.
So, the deviation becomes more visible when the dimensions of the aperture or the obstacle are comparable to the wavelength of light, and easily seen with the naked eye.

Step 2: The diffraction pattern obtained on the screen consists of a central maximum, and secondary minima.
The width of the central maximum is the distance between the first secondary minimum on either side of a point (let O) at which intensity of central maximum is highest.
The angular width of central maximum can be given by \[2\theta \] i.e.,
\[2\theta = \dfrac{{2\lambda }}{a}\] (1)
Where \[\lambda = \] wavelength of light falling on the slit
 \[a = \]aperture or width of the slit

Step 3: As given in the question –
\[\lambda = 5000A^\circ \] and \[a = 2 \times \mathop {10}\nolimits^{ - 5} \]m
So, putting these values in equation (1)
\[2\theta = \dfrac{{2 \times 5000 \times \mathop {10}\nolimits^{ - 10} }}{{2 \times \mathop {10}\nolimits^{ - 5} }}\]
\[2\theta = \dfrac{{2 \times 5 \times \mathop {10}\nolimits^{ - 10 + 5 + 3} }}{2}\]
\[2\theta = \dfrac{{2 \times 5 \times \mathop {10}\nolimits^{ - 2} }}{2}\]radian
\[2\theta = 5 \times \mathop {10}\nolimits^{ - 2} \]radian

$\therefore $ The total angular width of central maxima in this diffraction pattern is \[2\theta = 5 \times \mathop {10}\nolimits^{ - 2} \]radian.

Note:
The phenomena of diffraction are common to all types of waves. In the case of sound waves and radio waves, diffraction is observed readily because the wavelength of these waves is large, and obstacles of this size are easily available. But in the case of visible light, the wavelength is very small. So, the aperture of this size is not available easily and because of that diffraction of visible light is not so common.