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.