What is meant by the diffraction of light?

In physics, the term diffraction is defined as the bending of light around the corners of the obstacle. As a light ray passes by an aperture, it bends around the edges or through slits, it spreads out through a narrow opening. The diffracted light will produce fringes of bright and dark or colored bands which are labeled as a diffraction pattern.

Expression for diffraction of light

The expression for diffraction of light is,

                               nλ= d sinθ

Where,

d=Slit separation distance

θ=Diffraction angle

λ=Wavelength of light

n=Order of maximum

Types of diffraction

There are two types of diffraction,

• Fresnel diffraction–The diffraction in which the light source and slits are placed at a finite distance is called Fresnel diffraction. The incident and the diffracted wave fronts are either spherical or cylindrical.

• Fraunhofer diffraction-The phenomenon in which the light source and the slits are kept away from each other is called Fraunhofer diffraction. It depends only on the angle from the aperture to the screen. Here, the incident wave fronts and the diffracted wave fronts are planes.

Conditions for diffraction to occur

The one condition, which is fundamental for the occurrence of diffraction is the width of the obstacle or the slit must be less than or identical to the wavelength of the light used. If this condition is satisfied, bending of light takes place.

In case, if the obstacle has a straight edge, it should be sharp-edged or if it is a hole, its diameter must be tiny and most importantly, the thickness of the obstacle must be small or similar to the wavelength of the light.

Let λ is the light’s wavelength and a be the fringe width, the diffraction condition is given by,

                        $\frac{ \lambda }{a}=1 \left(or\right) \lambda =a$

Huygens principle

 The conceptualization of diffraction is described by Huygens's theory. He observed that every point on the wavefront acts as a source of secondary spherical wavelets, which spread out in the forward direction at the speed of light.

When you open your room window in the morning, the light enters your room and it spreads throughout the room. Do you know what happens? Because of the light’s wave nature, it comes over from the window and outspreads completely in all directions.

Important terms in diffraction

Phase difference

The difference between two light waves or any two objects which have the same origin and frequency is called phase difference. The unit is the radian.

Path difference

Path difference is the difference between the distance traveled by two waves from the source to the point where they meet. The unit is meter.

Constructive interference and destructive interference

When a light wave travels, the waveform forms two surfaces. In the waveform, the upper surface layer is called the crest and the lower surface is called the trough. When two waves travel together, if the crest of a wave meets the crest of another wave or the trough of a wave meets another trough, it produces a bright fringe. It is called constructive interference. If the crest of a wave comes in contact with the trough of another wave, it is known as destructive interference.

Constructive interference happens if the phase difference of the waves  is an even multiple of π (2, 4, 6…) and destructive interference happens if the phase difference of waves is an odd multiple of π (1, 3, 5..)

Fringe width

It is the difference between the two consecutive bright or dark fringes in the diffraction pattern.

Single slit experiment

In the double-slit experiment, there are two slits. If they replaced it with a single slit, we get a single broad fringe pattern with a bright region at the center of the fringe. This experiment is an exercise of Huygens's theory, which depicts that every point on the wavefront acts as a secondary source.

When the beam enters into the single slit, the slit thickness should be small than the light’s wavelength. As the light waves enter into the slit, it creates a diffraction pattern on the optical screen. Once the light ray enters the slit, it starts to act as a source and produces wavefronts. All the wavefronts produced here gathered together to create the diffraction pattern, which has dark and bright fringes.

Double-slit experiment

In classical physics, the double-slit diffraction experiment is an important one. The experimental setup consists of monochromatic light, a screen with double slits, and an optical screen. The laser beam is used as the light source because the light used to diffract the waves must be coherent. A beam of laser is made to pass through a screen that has two slits.

The light which comes from the opening of the slit act as coherent waves, and forms an interference pattern in the screen. The pattern produced includes dark and bright fringes. Because of the destructive and constructive interference, dark and bright fringes are formed.

Central maximum

In the single-slit experiment, when a ray of light enters into the slit, it starts to act as secondary waves, the source reinforces one another which results in the formation of maximum intensity at a particular point. The point is called central maximum.

Airy disk

When an array of light travels into any circular aperture or small opening, it forms a diffraction pattern on the film which consists of a bright region in the center surrounded by concentric circles of diminishing intensities. The center brighter region is called the airy disk.

Diffraction grating

In optical physics, grating is a fundamental application in diffraction. The device diffracts light into various wavelengths. When a white light encounters the grating, it diffracts into colors of various wavelengths as the light travels through a fine line of gratings, called reflection grating.

X-ray diffraction

Another application of X-ray diffraction is that it helps to identify the crystallographic structure and orientation of an unknown material. It is used to study the average spacing between layers or rows of atoms or molecules. We can also calculate the internal stress, shape, size of the tiny crystals.

 X-ray diffraction is a phenomenon in which an incident beam of X-rays when illuminated through the atomic planes of a crystal, therefore the planes collide with one another as they leave the crystal, the crystal structure is studied.

Resolving power of a telescope

Assume, we are going to observe a star in the sky by using a telescope. The light enters into the telescope via lens and passes by the circular opening or aperture, here the light gets diffracted. Because of the diffraction limit, the lens has the potential to diffract two objects which are arranged intact. When a star is viewed through a telescope it looks blurry due to the light being outspread. In order to get a clear picture, the bright central band of the first star should fall on the first dark band of the next star. We can get a clear image of the star, by increasing the lens power and also thereby it changes the telescope resolving power, and this phenomenon is called as rayleigh criteria.

The formula of the diffraction limit of any lens is,

$\sin \theta =\frac{\lambda }{D}$

Where

λ=wavelength &

D=len’s diameter.

Formulas

The diffraction of light is,

     n λ=d sin θ

The diffraction limit of any lens is,

$\sin \theta =\frac{\lambda }{D}$

Context and Applications

This topic is an important one in optical physics and for all the entire graduate and undergraduate students, particularly for, bachelors and masters in science (physics & chemistry) and bachelors in technology (electrical engineering).

Practice Problems

Question 1: For the second-order bright-line find the wavelength of the light which is used to illuminate a  grating that has 2000 lines/cm at a 30° angle.

1. $125000 \stackrel{0}{A}$                                     
2. 20000 $\stackrel{0}{A}$
3. $150000 \stackrel{0}{A}$                                     
4.  $950000 \stackrel{0}{A}$

Answer: The correct option is a.

Given data:

Number of lines in the grating N= 2000 lines/cm

Order n=2

The distance between the lines, $d=\frac{1}{N}$

                                                  $$\begin{gathered} d=\frac{1}{2000 lines/cm} \\ d=5\times {10}^{-6}m \end{gathered}$$

The angle of diffraction =30°

Explanation:

The formula of diffraction of light is,

                                                    n λ= d sin θ

Hence, the wavelength of the light is,

$$\begin{gathered} 2\lambda =5\times {10}^{-6}\times \sin 30° \\ \lambda ==\frac{5\times {10}^{-6}\times \sin 30°}{2} \\ \lambda =1.25\times {10}^{-6} \\ \lambda =125000 \stackrel{0}{A} \end{gathered}$$

The wavelength of the light is 125000 A°.                                            

Question 2: Bending of light rays is known as?

1. Reflection
2. Refraction
3. Diffraction
4. Polarisation

Answer: The correct option is c.

Explanation: The phenomenon of bending of light rays around the corners of an obstacle is called diffraction.

Question 3: A monochromatic light with a wavelength of $2.5\times {10}^{-7}$ m strikes a grating containing 10000 slits/cm. Determine the angle of the second-order bright line.

Answer: The correct option is a.

Given data:

Wavelength $\lambda =2.5\times {10}^{-7}m$

Number of slits N=$10000 slits/cm$

Order n=2

Explanation:

The distance between the lines, d=$\frac{1}{N}=\frac{1}{10000slits/cm}=1\times {10}^{-4} cm=1\times {10}^{-6}m$

Hence,

$$\begin{gathered} n\lambda =d\sin \theta \\ \left(2\right)\times \left(2.5\times {10}^{-7}\right)=(1\times {10}^{-6})\sin \theta \\ \sin \theta =\frac{\left(2\right)\times \left(2.5\times {10}^{-7}\right)}{1\times {10}^{-6}} \\ \sin \theta =0.5 \\ \theta =30° \end{gathered}$$

Question 4: In single slit diffraction, a circular aperture produces a diffraction pattern of concentric rings that grow fainter as we move away from the center is known as ______.

1. Airy discs
2. Circular discs
3. Single discs
4. None of these

Answer: The correct option is a.

Explanation: When a ray of light enters into a circular aperture it forms a diffraction pattern on the film which consists of a bright region in the center surrounded by concentric circles of diminishing intensities. The center brighter region is called the airy disk.

Question 5: From the given options, which are diffraction-limited devices?

1. Periscope
2. Microscope
3. Telescope
4. option (b) and (c)

Answer: The correct option is d.

Explanation: Microscope and telescope devices have resolving power. When the light enters into the aperture through the lens, the resolving potential of the lens diffracts the point source and produces a clear image for the view. In order to get a clear picture, the bright central band of the first image should fall on the first dark band of the next image. We can get a clear image of the object, when viewed through the device.