Does Frequency Affect Diffraction:How And Detailed Facts

In previous articles, we have studied in brief about diffraction and behavior of light and sound waves to cause diffraction. In this post, let us learn about the factors affecting diffraction.

Frequency refers to the number of waves passing towards a fixed point in a unit of time. Since diffraction occurs due to the wave striking the corner of the obstacle, does frequency affect diffraction as the wave has a certain frequency? If yes, then let’s learn the relation between frequency and diffraction and how does frequency affect diffraction in detail.

How does frequency affect diffraction?

Every wave propagating in a medium has a certain frequency that is inversely associated with the wavelength. However, we have learnt the influence of wavelength on diffraction; it is so obvious that frequency can also affect the diffraction.

Frequency is an invariable entity after the diffraction, i.e., the frequency of the incident wave does not change when the wave gets diffracted. However, the amount of diffraction depends on the frequency of the incident wave.

The wave with high frequency diffracts less than the wave with low frequency.

Since high frequency refers to shorter wavelength, in the phenomena of diffraction, always wave with greater wavelength diffract more rapidly than the short wavelength. Thus, the incident wave with low frequency must be incident to achieve greater diffraction.

If we consider the example of the sound wave, the following facts can be observed:

• When a high-frequency sound wave with a shorter wavelength strikes the obstacle, the waves do not diffract; instead, they reflect back around the obstacle, creating the shadow of sound behind the obstacle.
• The low-frequency sound strikes the obstacle; the wavelength of the incident wave is much longer than the barrier; thus, the wave can easily pass over the corner of the barrier, creating the wave’s diffraction.
• When a wave of frequency equal to the barrier dimension strikes, they create the mid-frequency range, and the waves are diffracted around the object. The edge of the object is used as the focal point and generates the new wave front whose frequency will remain the same, but the intensity is reduced.

Frequency and diffraction relationship

Though the frequency of the wave and diffracted wave remains the same before and after the diffraction occurs, diffraction always depends on the frequency. This dependency can be expressed by providing the relation between the frequency and diffraction as given below.

Let us suppose that a light wave of wavelength λ is passed through a slit of width d and the light wave s travels in a straight line to give the diffraction fringes.

The amount of diffraction can be given by the equation,

sinθ=λ/d

Where; θ is the angle between the incident and diffracted wave.

The wavelength can be given in terms of frequency as

f=c/λ

Where; c is the velocity of light. Rearranging the terms, we get frequency as

λ=c/f

Replacing the λ in the above equation; we get

sinθ=c/df

If we have considered the aperture as a circular aperture, the equation can be modified as

sinθ=1.22(c/df)

Where; 1.22 is the constant d is the diameter of the aperture and θ is the angle between the incident and diffracted wave.

If the angle θ is very small; then, sinθ~θ , then the equation will be

θ=1.22(c/df)

This gives the diffraction of the wave with a certain frequency of the incident wave. This gives the relation between the diffraction and frequency as they are inversely related. The equation we have obtained says that the diffraction is more if a wave of low frequency is incident on the aperture.

Frequently Asked Questions

What are the essential conditions needed for the diffraction of light?

The light undergoes diffraction if it possesses the conditions that are listed below.

• The light has to be monochromatic to achieve a perfect diffraction pattern. (The diffraction can be achieved using white light, but we get the dispersion of colors as a diffraction pattern).
• The wavelength of the light should match the width of the aperture used.
• The width of the slit should be sufficiently narrow to get good diffraction fringes.

Does diffraction cause interference?

Yes, in some cases, the diffraction can cause interference.

Interference refers to the superposition of two or more coherent light waves. If a monochromatic light wave is passed through a double slit, first they get diffracted at the corner of the slit, and then the two diffracted light waves superimpose on one another, causing the interference.

Are the fringes obtained from diffraction equally spaced?

The spatial arrangement of the fringes depends on the slit we have chosen for the diffraction experiment.

• In a single slit experiment, the fringes are not equally distributed. The width of the fringes we have obtained from the single slit is unequal, and its width decreases as it moves outward.
• In a double-slit experiment, the fringes are equally spaced as we get interference of the diffracted light; their width is also equal.

Does the angle of the incident wave affect the diffraction?

The angle of incidence does not affect the diffraction of the wave.

Diffraction is a wave phenomenon that depends on the wavelength, frequency of the wave and the linear dimension of the hurdle. The angle at which the wave has incident does not matter for the wave to get diffracted.

Do the properties of the wave remain the same after the diffraction?

Diffraction is the process that does not change any properties of the wave. It slightly changes the direction of the wave.

When a wave of specific wavelength, frequency, and speed strike an obstacle, the wave changes its direction, causing the bending of the wave. The properties like speed, wavelength, frequency and time period remain unaltered even after the diffraction.

How does the refractive index of the medium affect the diffraction?

Diffraction is a spatial phenomenon that occurs due to the invariant properties of the wave medium.

The wavelength of the wave inversely varies with the refractive index of the medium, i.e., the medium which possesses a high refractive index, the wave travelling in the medium should possess a shorter wavelength—the shorter wavelength results in less thus high refractive index medium exhibit low diffraction.

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