Diffraction Of Light Waves

Introduction

Diffraction of light waves is an important concept of wave optics. The phenomena of light, reflection and refraction can be explained only on the basis of wave optics. The direction in which the light propagates in the form of a wave is indicated by the light screen itself. When a stone is dropped on a motionless surface of the water, ripples spread around the area where the stone falls.

This event is a perfect example of a wave spreading. As the ripple passes a particular point, the water molecules or particles at that point move up and down (or oscillate). All nodes of a wave equidistant from a focal point have a wavefront that resonates in phase.

What is Diffraction?

• A common characteristic of all waves like sound waves, light waves and water waves is diffraction.

• The phenomenon in which the wave bends around the edge of an obstacle and travels within the geometric shadow of the obstacle is called diffraction.

• A ray of light passing through a medium follows a straight path without any bend. But the diffraction occurs only when the size of the obstruction is comparable to the wavelength of the wave.

• In order for diffraction to occur in the light, the size of the obstruction must be comparable to the wavelength of the light.

• Depending on the shape of the resulting wavefront, the diffraction can be classified into two types.

  • Fresnel Diffraction

  • Fraunhofer Diffraction

What is a single slit diffraction?

• Consider a parallel beam of light incident perpendicularly on a single slit of width AB.

• A diffracted light beam falls on a screen placed at a distance called the center of the slit.

• A straight line passing through point C perpendicular to the plane of the slit reaches a point on the screen. The light intensity of any point i.e. point P on the screen can be found.

• The straight lines reaching P from different points of the slit can be considered as parallel lines making an angle of θ with the vertical line.

• Parallel light waves from different points of the slit intersect at point P and other points on the screen to give the resultant light intensity.

• Point P is in the shaded region of the geometry. Due to diffraction, the central maximum is seen extending up to this region.

• Point P on the screen should find the conditions for achieving different minima.

• If the slit is divided into an even number of small parts, the path differences of the light waves from the parts add up and cause destructive interference at the point P, producing minimum light intensity.

• To explain the maxima, the slit should be treated as odd-numbered segments.

Single Slit Diffraction Formula

Slit AB should be divided into two halves AC and CB. Now the width of AC is (a/2). Different points of width in the gap (a/2) are called corresponding points.

Light waves from different points overlap at point P and cause destructive interference, causing the first minimum. The path difference of light waves from similar points,

$$\mathrm{\delta =\frac{a}{2} sinθ}$$

$$\mathrm{Condition\: for\: point\: P\: to\: be\: the\: first\: minimum}$$

$$\mathrm{\frac{a}{2} sinθ=\frac {\lambda }{2}}$$

$$\mathrm{BN= a\:sinθ=\lambda (first\: minimum)}$$

$$\mathrm{Condition\: for\: point\: P\: to\: be\: the\: second\: minimum}$$

$$\mathrm{\frac{a}{4}sinθ=\frac {\lambda }{2}}$$

$$\mathrm{BN= a\: sinθ=2\lambda (second\: minimum)}$$

$$\mathrm{Condition\: for\: point\: P\: to\: be\: the\: nth\: minimum}$$

Divide the slit into 2n equal parts. The condition for the nth minimum to occur where a light wave from a similar point is cancelled by a light wave from another similar point is,$ \mathrm{\frac{a}{2n} sinθ=\frac{λ}{2}}$

$$\mathrm{a\: sinθ=n\lambda (nth\: minimum)}$$

The Central Maximum

In order to achieve the maximum, the slit must be divided into odd-numbered equal parts. By dividing in this way the light wave coming from any similar point is not destroyed and hence the point P will be of maximum intensity.

$$\mathrm{The\: condition\: for\: the\: first\: maximum,}$$

$$\mathrm{\frac{a}{3}sinθ=\frac{λ}{2}}$$

$$\mathrm{a\: sinθ=\frac{3λ}{2}}$$

$$\mathrm{The\: condition\: for\: the\: second\: maximum,}$$

$$\mathrm{\frac{a}{5} sinθ=\frac{λ}{2}}$$

$$\mathrm{BN = a\: sinθ=\frac{5λ}{2}}$$

Similarly, the condition for the nth maximum

$$\mathrm{a\: sinθ=(2n+1)\frac{λ}{2} (nth\: maximum)}$$

The central maximum is called the zeroth order maximum. Maximum intensity is found almost between the successive minima.

Conclusion

The phenomena of light, reflection and refraction can be explained only on the basis of wave optics. A common characteristic of all waves like sound waves, light waves and water waves is diffraction. The phenomenon in which the wave bends around the edge of an obstacle and travels within the geometric shadow of the obstacle is called diffraction.

A ray of light passing through a medium follows a straight path without any bend. But the diffraction occurs only when the size of the obstruction is comparable to the wavelength of the light. The central maximum is called the zeroth order maximum. Maximum intensity is found almost between the successive minima.

FAQs

1.Define interference of light

When two light waves overlap each other, the phenomenon of light intensity increasing at some points and the light intensity decreasing at other points is called interference of light.

2.Explain the scattering of light

Scattering or scattering of electromagnetic radiation refers to the scattering of light waves in unexpected directions as they travel through a light-medium, through defects in the medium or at the interface with another medium.

3.Why is the colour of the clear sky blue?

During the day, the shorter wavelength blue colour is scattered throughout the atmosphere by atmospheric particles. Also, human eyes are more sensitive to blue than purple. It is due to such reasons that the sky appears blue.

4.Explain Maxwell's Electromagnetic theory

• Maxwell demonstrated that light is an electromagnetic wave carrying electromagnetic energy that propagates in the form of interference. According to Maxwell’s theory, light is an electromagnetic wave.

• Also, Maxwell was able to prove that electromagnetic waves do not need any medium to propagate. This approach proved successful in all cases of light.

5.Why do oil films and soap bubbles on water exhibit fascinating colours?

The reason for these colours is the interference of the white light rays that are reflected multiple times between the surface and the base of the thin film. These colors depend on the angle of incidence of light, the refractive index of the film and the thickness of the film.

6.What is diffuse reflection?

• When light hits a rough surface, the light is scattered in many directions by the fine ridges on the surface. This type of reflection is called diffused reflection. Thus, no image is formed automatically, they reflect from each object.

• The shape of light depends on the surface from which it reflects. A common example of diffuse reflection is Lambertian reflectance.

7.What are the properties of electromagnetic waves?

• Electromagnetic waves are generated by accelerated electric particles. This scattering occurs due to the deflection of waves.

• These waves are not mechanical waves because they can propagate without the help of any medium.

• The speed of these waves is equal to the speed of light in a vacuum.