What is Diffraction? – Single Slit Experiment and Huygens Principle

Diffraction

Diffraction, polarisation and interference are the three major concepts essential for light wave nature.

What is diffraction? Diffraction is the phenomenon that enables the light radiated by a source to be easily detectable even though there is an obstacle in between. Here, the light acts like water, which flows around the obstruction to reach our eyes. 

Moreover, it does not necessarily mean that the light stream must flow around the obstacle.

In many cases, especially when an obstacle is very large, the stream of light does not flow around it. 

This article will deeply discuss the diffraction phenomenon while explaining other related concepts and topics.

Huygens’ Principle

In the 17th century, a Dutch mathematician named Christian Huygens declared that light is not capable of behaving like a particle. He suggested that the light behaves like a wave. His statement was contradictory to Newton’s beliefs. He postulated a principle named Huygens’ Principle, stating that each point on a light wave could act as a source for a secondary wave capable of travelling at the same speed as light.

Furthermore, he managed to explain the optical phenomena occurrence, namely reflection and refraction, using his light wave theory. However, he failed to illustrate the light’s wave nature, making it impossible for him to claim his achievement experimentally.

After nearly a decade, there came Thomas Young, a very enthusiastic British polymath who successfully illustrated the behaviour of light. He made light squeeze through two slits kept adjacent to one another. We call squeezed light an interference pattern, which can be seen as a uniform, alternating pattern of dark and bright bands.

This discovery by Thomas Young vindicated Huygens. He proved that it is impossible to bend light or make it flow around an obstacle unless it obeys the Huygens principle. He said such a pattern could only be formed by waves interfering with one another.

A bright band is created while squeezing two waves between the slits. Here, one ripple’s peak interferes with another’s.

In addition, when a ripple peak interferes destructively with another one, it can form a dark band. The addition doubled the region’s luminosity while the negation rendered the region fully dark.

It is a phenomenal discovery because it also helps produce the pattern using a single slit. But, unlike the pattern produced by two slits, the light’s intensity does not seem to be distributed evenly in a single slit. We call this diffraction pattern because the light is diffracted (where it is painted).

Single Slit Experiment

Two conditions need to be fulfilled to ensure the phenomenon is observable. When the wavelength of the light is larger or similar to the obstacle, there produces a diffraction pattern. The light will pass without touching if the slit’s width is very large. As a result, a bright spot is illuminated on the screen.

On the other hand, if the slit is narrow, the light can be spectacularly diffracted.

See the following figure to understand it better:

As discussed earlier, the waves can bend and change their direction. While doing so, they seem to spread, causing mimic ripples. Commonly, the ripples get approximated using parallel lines because the waves can be seen as straight lines since the screen is kept far away. 

Based on Huygens’ principle, it is proved that all the points between the edges act as sources of waves. The interference pattern given above can be generated depending on the interference of two completely different waves that emanate from two dissimilar slits. As a result, a diffraction pattern is created from a single source.

Its working includes the interference of secondary waves with one another when they bend around the slit. Bending makes the wave travel much longer than the other wave. 

Let us consider the parallel rays that bend at an angle with the slit.

There will be a formation of value at the bending point of the two waves. These waves either interfere destructively and produce a small dark region or negate one another completely. As a result, one wave’s peak can be seen superimposed on the other one’s valley.

The Distance of Separation

The waves produced by the first point do not travel an equal distance. Here, the waves are capable of interfering destructively to generate a minimum. The following is the representation of the same:

sin  (a)  = ± n for n = 1, 2, 3

This equation is mainly suitable for waves that could bend at different angles. When those waves satisfy this equation, they interfere destructively. From the above equation, n is represented as the integer that denotes the order of the minimum. 

It is possible that the first-order minimums can be generated on either side when sin  a = ± λ / d. Meanwhile, the second minimums are usually produced on either side when sin a =± 2 λ / d and so on. There is a maximum between each minimum. Finally, at n = 0 is the point where the central maximum is generated. 

Moreover, two maximums work together to flank this minimum, which makes the central maximum wider compared to the others. In terms of sin  (a), it is 2 λ / d.

Take a look at the following diagram:

From this figure, we can observe that the screen and the slit are kept separated at a distance of D. It has a humongous magnitude compared to the width of the slit, which is denoted by ‘d’. Here, β the angle formed between two waves produces the first minimum. The first minimum can be seen at a distance y (1) from the axis. It can be given as:

β = y 1 / D 

The β angle is very small, so we write it as cos  (β)  ≈ 1. It indicates that sin  (β)  ≈ (β). Since it is too small, it can be termed sin  (α)  ≈ (β), such that α ≈ β. 

Keep in mind that, for the first minimum:

sin α  =λ / d 

Hence,

λ(1) /D = λ /d

From that, we can imply that the screen distance D and wavelength y are constant. When the distance y is increased or the pattern becomes wider, the slits can get narrower. Therefore, when the slit is kept narrow, the diffraction of light is done spectacularly.

The Intensity

The following is the expression for a diffraction pattern’s intensity of a maximum:

From the above expression, I0 is considered a constant with a value proportional to the square light’s amplitude.

The value of α  for the minimums is ± n=λ/ d. While substituting that in the expression, the numerator will be reduced to (πn). It equals zero. Later, the value of sin  (α) for maximums will be equal to (n + 1 / 2 )λ /d. Both the waves (interfere constructively and destructively) can travel the same distance. Therefore, they are generally halfway between the minimums.

The following graph shows the intensity curve:

Diffraction Grating

A symmetric pattern is produced when the light appears to be coherent and monochromatic. The pattern produced can have multiple colours, like a rainbow. An ideal example of this would be CDs. 

A CD can be composed of equally distanced parallel wires. They are extremely thin. The gaps present in them act as slits while illuminating. We can compare the width of each slit. They appear to be smaller than the light’s wavelength. Hence, all those slits can diffract light naturally. In the optics field, especially in the series of incredibly thin, we call the equidistant parallel wires diffraction grating.

Conclusion

All in all, diffraction is nothing but the bending of a wave around obstacles. It is a very important concept in wave optics. From this blog, we have understood the diffraction definition and how the Huygens principle plays a major role in the diffraction phenomena.

In addition, we have also learned what single slit diffraction is, along with a comprehensive knowledge of the intensity, the distance of separation and diffraction grating.

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