How to Measure Wavelength Using Young’s Interference Bands

A laboratory experiment to measure wavelength by Young’s interference bands is shown in the diagram below. Light from a small filament lamp is focused by a lens on to a narrow slit S, such as that in the collimator of a spectrometer. Two narrow slits A, B, about a millimetre apart, are placed a short distance in front of S, and the light coming from A, B is viewed in a low-powered microscope or eyepiece M about two metres away. Some coloured  are then  observed by M.A. red and then a blue filter, F, placed in front of the slits, produces red and then blue bands. Observation shows that the separation of the red bands is more than that of the blue bands. Now λ= ay/D, from (ii), where y is the separation of the bands. It follows that the wavelength of red light is longer than that of blue light.

In order to accurately measure wavelenth, we must know that an approximate value of the wavelength of red or blue light can be found by placing a Perspex rule R in front of the eyepiece and moving it until the graduations are clearly seen, Fig. 1. The average distance, y, between the bands is then measured on R. the distance a between

the slits can be found by magnifying the distance by a convex lens, or by using a travelling microscope. The distance D from the slits to the Perspex rule, where the bands are formed, is measured with a metre rule. The wavelength λ can then be calculated from λ = ay/D, and is of the order 6 x 10-5cm. 

The wavelengths of the extreme colours of the visible spectrum vary with the observer. This may be 4 x 10-5cm for violet and 7 x 10-5cm for red; an “average” value for visible light is 5.5 x 10-5cm, which is a wavelength in the green.

Appearance of Young’s Interference Bands     

The experiment just outlined can also be used to demonstrate the following points:-

If the source slit S is moved nearer the double slits the separation of the bands is unaffected but their intensity increases. This can be seen from the formula y (separation) = λD/a. since D and a are constant.

If the distance apart a of the slits is diminished, keeping S fixed, the separation of the bands increases. This follows from y = λD/a.

If the source slit S is widened the bands gradually disappear. The slit S is then equivalent to a large number of narrow slits, each producing its own band system at different places. The bright and dark bands of different systems therefore overlap, giving rise to uniform illumination. It can be shown that, to produce interference bands which are recognizable, the slit width of S must be less than λD1/a, where D1 is the distance of S from the two slits A, B.

If one of the slits, A or B, is covered up, the bands disappear.

When we measure wavelength with white light, the central band is white, and the bands either side are coloured. Blue is the colour nearer to the central band and red is farther away. The path difference to a point O on the perpendicular bisector of the two slits A, B is zero for all colours, and consequently each colour produces a bright band here. As they overlap, a white band is formed. Farther away from O, in a direction parallel to the slits, the shortest visible wavelengths, blue, produce a bright band first.    

Young’s Interference Bands

Light passing through two narrow slits and falling on a screen produces a pattern of bright and dark regions, called fringes. The shape of the fringes depends on how the waves interfere.

In 1803, Thomas Young performed an experiment which demonstrated the wave nature of light. He shone monochromatic light through a small pin hole onto a double slit. This experiments produced bands of light and what we now know as the Young’s Interference bands.

Young's Interference bands

Constructive Interference

Passing a beam of monochromatic light through two narrow slits (an experiment first performed in 1801 by Thomas Young) shows that light exhibits both ray and wave behavior. As the light diffracts through the slits it produces a pattern of bright and dark bands on a screen. These bands are caused by constructive and destructive interference of the overlapping waves. This effect is observed with all waves, including sound and water, as well as light.

The basic idea of constructive and destructive interference in the Young’s Interference bands concept, is that when two waves overlap, their amplitudes can be increased through constructive interference or diminished through destructive interference. The resulting wave may be higher, lower or the same as the original. The amount of overlapping depends on the phase difference between the two waves. If the phase difference is zero, then the two waves are perfectly in phase and they interfere constructively. If the phases are opposite, then the waves cancel each other out and there is no resulting wave.

This is a general rule that can be applied to any pair of waves, whether they are identical or not. However, it is important to remember that the phase difference between the two waves determines how the resulting interference pattern will look, not their relative amplitudes. This is because the amplitudes of the individual waves are not additive, they are multiplicative, meaning that each new wave added to the previous one increases the total amplitude of the system.

Constructive interference (Young’s Interference bands) is only possible if the crests and troughs of the two waves match up exactly and are exactly in phase with each other. If the crests are not in phase with each other then they cancel each other out, and if the troughs are not in phase then they will interfere destructively and decrease the total amplitude of the system.

The other factor that determines the outcome of the interference is the distance between the two source points. If the two sources are closer together then they will be in phase and will produce constructive interference. If the two sources are farther apart then they will be out of phase and will produce destructive interference. The exact distance between the two sources will depend on the speed of the light and the wavelength of the light, as well as other factors such as how fast the light is moving through the medium.

Destructive Interference

The wave interference pattern(Young’s Interference bands), we observe in Young’s double slit experiment depends on the relative phase of the waves and their path length differences. When waves interfere constructively, they add to each other, resulting in a larger wave with increased amplitude. When they interfere destructively, however, the waves cancel each other out, resulting in a smaller wave with decreased amplitude.

This is why we see bands of bright and dark fringes in the interference pattern. The bright fringes result from constructive interference, and the dark fringes are produced by destructive interference.

Constructive interference occurs when the crests of one wave align with the troughs of the other wave. When the peaks and troughs of the two waves are not in alignment with each other (meaning they are 180-degrees, or half a wavelength, out of phase), the resulting wave has a decreased amplitude, and may even be canceled out altogether. The resulting combined wave will have crests that are shorter and shallower than the crests of either of the original waves, as shown in the image above.

To understand how the phase difference between two waves can create both constructive and destructive interference, consider the example of a walkie talkie signal. If the transmitter and receiver of the walkie talkie are exactly in phase, the resulting wave will be additive, and the amplitude of the incoming signal will increase. If the two transmitters are not in phase, however, the resulting wave will be subtractive, and the amplitude of the resulting signal will decrease or disappear entirely.

The same principle applies to light waves, and it is the reason that we see bands of bright and dark interference patterns in Young’s experiment. The different colors seen in the soap bubble are due to the interference of the reflected light from the inside and outside surfaces of the thin soap film. The reflected light interferes both constructively and destructively with the light bouncing around within the soap bubble, creating both the iridescence of color and the interference bands observed in the bubble.

This is why the spacing between the different interference fringes varies depending on the width of the separation between the two slits, as shown in the diagram below. As d increases, the fringes move closer together, and vice versa.

The Double Slit Experiment

Two very narrow parallel slits separated by a distance equal to the wavelength of light are cut into a thin sheet of metal. A single, monochromatic light source is placed behind the slits. The light passes through the slits and falls on a screen a large distance away from the slits. The light from each slit diffracts and overlaps with the other, producing an interference pattern on the screen. If the waves are out of phase they cancel each other out, producing a dark patch on the screen. If they are in phase, the pattern produces bright bands on the screen.

Young’s experiment demonstrated that light behaves like a wave and not as a particle. If you were to replace the photons in his experiment with grains of sand or other particles, they would appear as pinpricks on the sensor screen instead of the interference pattern seen with the photons. This would be a very strong demonstration that particles, not photons, make up matter.

When the light waves from slits 1 and 2 are in phase they create bright bands on the screen. The brightening of the band occurs because the waves have a phase difference that gives rise to constructive interference on the far side of the slits. The phase difference between the waves is the product of their wavelength and the separation between slits (or the screen distance, D). The higher the order of the interference pattern, the greater the intensity.

If the light waves from slits 1 & 2 are out of phase, they will cancel each other out and produce a dark patch on the screen. The phase difference between the waves is the inverse of their wavelength and the separation between slits. The polarization of the light is also a factor.

If you place a mirror at the screen distance from the first slit, the interference pattern becomes more pronounced and the light reflects off the mirror into the viewer’s eye. The light reflecting off the mirror will be at a different angle to the interference pattern on the screen, giving a more distinct and pronounced reflection.

The Interference Fringes

When two waves interfere with each other, they produce a pattern of light and dark bands on a screen. The shape of these fringes depends on whether they interfere constructively or destructively. A tall, skinny wave will have more constructive interference, while a short and wide wave will have more destructive interference. The shape of the fringes also depends on the wavelength of the light used in the experiment. The longer the wavelength, the closer together the fringes will be.

Young’s double slit experiment was the first to provide quantitative evidence that light can behave either as a wave or as a stream of particles depending on the circumstances. The experiment uses a monochromatic beam of light shone through a pinhole on one board, and then onto a second screen with two closely spaced slits. The light emerging from the second slit produces a pattern of bright and dark bands that cannot be explained by Newton’s theory that each particle passes through the slit independently. Young concluded that the light must be a wave phenomenon.

Today’s classroom versions of this experiment use a slide with two etched slits instead of a note card with a pinhole. This change in the experiment allows a more reliable measurement of the distance between the slits, known as the d value in Young’s equation. This value is needed in order to determine the wavelength of the light being used.

The brightness of the central bright fringe in the image below is determined by the fact that the light from both slits travels the same distance to the screen, which is a result of constructive interference. The darker fringes on both sides of the zero-order fringe are a result of destructive interference, because the light from one slit travels a distance that is 1/2 a wavelength longer than the distance that the light from the other slit travels. As a result, crests from one slit meet troughs on the other slit, creating a dark fringe.

When a wave has two components with different frequencies, the resulting effect is called a beat. In this case, the components of the wave interfere with each other to create a pattern of alternating dark and bright bands on the screen. In order for this interference to occur, the two waves must have the same polarization.