Diffraction Of Light

Diffraction

Diffraction of light refers to the bending and spreading of light waves when they encounter an obstacle or pass through a narrow aperture. This phenomenon is a fundamental concept in wave optics and plays a crucial role in understanding the behaviour of light. In everyday life, diffraction can be observed in the spreading of light from a streetlamp through a fog, the patterns seen when light passes through a fine mesh or slit, and the iridescent colours of a CD or DVD.

The phenomenon of bending of light around the corners of an obstacle of the size of the wavelength of light is called diffraction.

The phenomenon resulting from the superposition of secondary wavelets originating from different parts of the same wavefront is defined as a diffraction of light.

Diffraction is the characteristic of all types of waves.

The wavelength of the wave is directly proportional to its degree of diffraction.

From the above figure, we can say that if slit width is more then wave will detract less.

Condition for Diffraction

For diffraction to occur, several conditions must be met:

1. Wave Nature of Light: Light must be treated as a wave phenomenon rather than a particle phenomenon.

2. Obstacle or Aperture Size: The size of the obstacle or aperture must be comparable to the wavelength of the light. If the obstacle or aperture is much larger than the wavelength, diffraction effects will be minimal.

3. Coherent Light Source: The light source should be coherent, meaning that the light waves should have a constant phase difference and the same frequency. This is often achieved using monochromatic light sources, such as lasers.

4. Narrow Aperture or Sharp Edges: The aperture should be narrow, or the edges should be sharp, to observe significant diffraction patterns. This allows the light waves to bend around the edges and interfere with each other, creating visible diffraction patterns.

When these conditions are met, diffraction causes light waves to spread out and create interference patterns, which can be observed as a series of bright and dark fringes. This principle is applied in various fields such as microscopy, astronomy, and the design of optical instruments.

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Solved Examples Based on Diffraction of Light

Example 1: The penetration of light into the region of geometrical shadow is called :

1)Polarization

2) Diffraction

3)Interference

4)Refraction

Solution:

Diffraction - The phenomenon of bending of light around the corners of an obstacle of the size of the wavelength of light is called diffraction.

So, the penetration of light into the region of the geometrical shadow is called diffraction

Hence, the answer is the option (2).

Example 2: The orange light of wavelength $6000 \times 10^{-10} \mathrm{~m}$ illuminates a single slit of width. The maximum possible number of diffraction minima produced on both sides of the central maximum is______.

1) 198

2)99

3)45

4)30

Solution:

Condition for minimum,
$
\begin{aligned}
& d \sin \theta=n \lambda \\
& \therefore \sin \theta=\frac{\mathrm{n} \lambda}{\mathrm{d}}<1 \\
& \mathrm{n}<\frac{\mathrm{d}}{\lambda}=\frac{6 \times 10^{-5}}{6 \times 10^{-7}}=100
\end{aligned}
$
$\therefore \quad$ Total number of minima on one side $=99$
Total number of minima $=198$

Hence, the answer is the option (1).

Example 3: In free space, an electromagnetic wave of 3 GHz frequency strikes over the edge of an object of size $\frac{\lambda}{100}$, where $\lambda$ is the wavelength of the wave in free space. The phenomenon, which happens there will be

1)Reflection

2)Refraction

3)Diffraction

4)Scattering

Solution:

For reflection size of the obstacle must be much larger than the wavelength, for diffraction size should be in order of wavelength and for scattering size of the obstacle must be smaller than the wavelength of the wave.

When an electromagnetic wave of frequency strikes over the edge of an object its wavelength gets changed due to the electromagnetic wave being absorbed. Then this phenomenon is known as scattering. Since the object is of size $\frac{\lambda}{100}$ much smaller than the wavelength $\lambda$, scattering will occur.

Hence, the answer is the option (4).

Example 4: A beam of light of wavelength 600 nm from a distant source falls on a single slit 1.00 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between the first dark fringes on either side of the central bright fringe is

1)1.2 cm

2)1.2 mm

3)2.4 cm

4)2.4 mm

Solution:

$
\lambda=600 \mathrm{~nm}=6 \times 10^{-7} \mathrm{~m}, \mathrm{a}=1 \mathrm{~mm}=10^{-3} \mathrm{~m}, \mathrm{D}=2 \mathrm{~m}
$

Distance between the first dark fringes on either side of the central bright fringe $=$ width of central maximum
$
=\frac{2 \lambda \mathrm{D}}{\mathrm{a}}=\frac{2 \times 6 \times 10^{-7} \times 2}{10^{-3}}=24 \times 10^{-4} \mathrm{~m}=2.4 \mathrm{~mm}
$

Hence, the answer is the option (3).

Example 5: Diffraction pattern from a single slit of width 0.25 mm is observed with light of wavelength 4890 Angstrom. The angular separation between first-order minimum and third-order maximum, falling on the same side, is:

1) $5.89 \times 10^{-3} \mathrm{rad}$
2) $5.89 \times 10^{-7} \mathrm{rad}$
3) $5.89 \times 10^{-10} \mathrm{rad}$
4) $5.89 \times 10^{-4} \mathrm{rad}$

Solution:

In a single slit diffraction pattern, positions of secondary maxima and minima are given by,

$\theta_{\max }= \pm(2 \mathrm{n}+1) \frac{\lambda}{2 \mathrm{~d}}$ and $\theta_{\min }= \pm \mathrm{n} \frac{\lambda}{\mathrm{d}}$, respectively.
$\therefore \quad \theta_{1 \min }=\frac{\lambda}{\mathrm{d}}$ and $\theta_{3 \max }=\frac{7 \lambda}{2 \mathrm{~d}}$
Angular separation
$
\begin{aligned}
& \text { Angular separation }=\theta_{3 \max }-\theta_{1 \min }=\frac{7 \lambda}{2 \mathrm{~d}}-\frac{\lambda}{\mathrm{d}} \\
& =\frac{5 \lambda}{2 \mathrm{~d}}=\frac{5}{2} \times \frac{5890 \times 10^{-10}}{0.25 \times 10^{-3}}=5.89 \times 10^{-3} \mathrm{rad}
\end{aligned}
$

Hence, the answer is the option (1).

Summary

Diffraction of light is the bending and spreading of light waves when they pass through a narrow aperture or around an obstacle, revealing the wave nature of light. This phenomenon is crucial for understanding various optical behaviours and is observable in everyday life, such as in the patterns seen when light passes through a fine mesh or the iridescent colours on a CD. Diffraction principles are applied in numerous fields, including microscopy, astronomy, and the design of optical instruments, enhancing resolution and providing deeper insights into the structure of matter.