Youngs experiment

Waves which leave two different points, S1 and S2, in phase will generally not be in phase as they arrive at a point P. The light intensity is greatest at points where the overlapping waves are in phase and interfere constructively. Light waves from the slits travel along different paths. If the path difference between waves travelling from slits S1 and S2 is zero or any whole number m of wavelengths to a point P on the screen, the waves will be in phase at that point.

In the more familiar version of Young's apparatus, the piece of card is replaced by a pair of narrow slits. In the typical set-up illustrated in Figure 8.8, light from a lamp is diffracted at a single slit

Young s fringes.

Courtesy of Chris Phillips, and illuminates two secondary Physics, Department Imperial slits. Light from these slits overCollege, London. laps and interference bands appear

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Figure 8.8 Double slit interference.

screen

Figure 8.8 Double slit interference.

on a screen behind the slits. We can obtain a value for the wavelength of light by measuring the spacing between the bands.

Path difference = S2A

If the separation of the slits is very much smaller than the distance between the slits and the screen (d <<< D),

SA S1S2

For constructive interference d0 = ml m is the 'order' of interference and is an integer (m = 1,2,3 ... ).

The bright points on the screen form of a series of narrow, equally spaced bands.

In Figure 8.8, 0 ~ tan 0 = —. Bright lines are found at distances y = D1, 2D1, 3D1 from the centre of the screen. d d d

We can measure the spacing between adjacent lines

D l d to obtain a value for the wavelength of the light.

In more general terms, when two waves of equal amplitude are superimposed, the size of the disturbance is somewhere between twice the amplitude of one wave (completely in phase) and zero (completely out of phase). If the waves are in phase at the centre of the screen the light intensity is maximal at that point. As we move out laterally from the centre, the phase difference between the waves gradually changes. The total amplitude decreases smoothly towards zero, where the light intensity is minimal, and subsequently increases smoothly to its maximum value. The cyclic variation of amplitude is repeated across the screen, giving rise to the broad, regularly spaced, alternately bright and dark bands. Figure 8.9 shows the bands as they are seen on the screen and also (underneath) how the light intensity varies laterally across the bands.

Sunlight (as used in Newton's experiment) creates multicoloured bands because it contains a more or less continuous spectrum of wavelengths and it is very difficult to obtain anything other than a

central bright fringe

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