# Young's Double Slit Experiment

Young’s double slit experiment uses two coherent sources of light placed at a small distance apart, usually only few orders of magnitude greater than the wavelength of light is used. A screen or photo detector is placed at a large distance â€™Dâ€™ away from the slits as shown.

## Young’s Double Slit Experiment

The original Youngâ€™s experiment used diffracted light from a single source passed into two more slits to be used as coherent sources. Lasers are commonly used as coherent sources in modern day experiments.

Each source can be considered as source of coherent light waves. At any point on the screen at a distance â€˜yâ€™ from the center, the waves travel distances $l_1$ and $l_2$ to create a path difference of Î”l at the point in question. The point approximately subtends an angle of Î¸ at the sources (since the distance D is large there is only a very small difference of the angles subtended at sources).

From the diagram it can be seen that the path difference can be expressed approximately as

$âˆ†l = d~ sin~Î¸$

Also observe that,

$tan~Î¸$ = $\frac{y}{D}$

However if we consider small values of Î¸, we can approximate the expression as

$tan~Î¸$ â‰ˆ $Î¸$ â‰ˆ $\frac{y}{D}$

Similarly $sinÎ¸$ â‰ˆ $Î¸$ for small values of $Î¸$. (See our videos on the Taylor Series)

Thus,

$âˆ†l$ â‰ˆ $d ~Î¸$ â‰ˆ $d \frac{y}{D}$

### Constructive and Destructive interference by Young’s double slit experiment:

For constructive interference, the path difference must be an integral multiple of the wavelength.

Thus for a bright fringe to be at y,

$nÎ»$ = $\frac{yd}{D}$

Or

$y_{n^{th}}$ = $n~\frac{Î»D}{d}$

Where $n$ = $Â± 0, 1, 2, 3â€¦..$

The $0^{th}$ fringe represents represents the central bright fringe.

Similarly, the expression for a dark fringe can be found by setting the path difference as

$âˆ†l$ = $(n~+~\frac{1}{2})Î»$

This simplifies to

$y_{n^{th}}$ = $(n~+~\frac{1}{2})~\frac{Î»D}{d}$

Note that these expressions require that Î¸ be very small. Hence $\frac{y}{D}$ needs to be very small. This implies D should be very large and y should be small. This in turn, requires that the formula works best for fringes close to the central maxima. In general for best results $\frac{d}{D}$ must be kept as small as possible for a good interference pattern.

The double slit experiment was a watershed moment in scientific history because it firmly established that light indeed behaved as a wave. The Double Slit Experiment was later conducted using electrons, and to everyoneâ€™s surprise, the pattern generated was similar as expected with light. This would forever change our understanding of matter and particles, forcing us to accept that matter like light also behave like a wave.

#### Practise This Question

Find the reading of the spring balance shown in figure. The elevator is going up with an acceleration of g/10, the pulley and the string are light and the pulley is smooth.