Objectives:

• To learn about and understand the Young double-slit experiment using visible light
(you should understand that this experiment gave a classical confirmation of the wave-nature of light) (Internet research on the ideas of Newton and Huygens about the nature of light);
(i)  $\lambda = \frac{ax}{D}$  for all waves where  $a$  <<  $D$  (a is slit width)
(ii) techniques and procedures used to determine the wavelength of light using a double-slit

The Young’s slit experiment could be used to find experimentally the wavelength of a light source and to prove that light behaves like a wave. A beam of light is shone on a pair of parallel slits placed at right angles to the beam. Light diffracts and spreads outwards from each slit into the space beyond. The light from the two slits overlaps and interfere with each other to generate and interference pattern of light and dark bands called fringes on the screen behind the slits.

In order for the experiment to work, the light source has to be coherent and of the same frequency. The ideal source is a LASER (Light Amplification by Stimulated Emission of Radiation) which has the same wavelength and therefore colour, and it is coherent. The horizontal width (on the diagram) of light of the fringes represent the intensity of the light. The $n_{0}$ maxima is going to be most intense. The green lines it’s the path light takes and the path from the slit underneath will travel longer than the one from the one above. At the $n_{0}$ maxima, the two waves will have traveled the same distance so that’s going to be the bigger, most intense maxima. Given that the two triangles (orange and green) are similar, we can say:

$\frac{ n \lambda}{a} = \frac{x}{D}$

$n$ is an integer value and represents the number of complete wavelengths out of phase the two waves will be by the time it reaches the screen with the fringes on. The $n_{1}$ fringe represents the two waves constructively superimposing for the first time (excluding the $n_{0}$) and so the two waves are $1 \lambda$ out of phase. Therefore, in the diagram above, $n = 1$ and so the equation becomes:

$\frac{ \lambda}{a} = \frac{x}{D}$

This can be rearranged for $\lambda$:

$\lambda = \frac{xa}{D} where$latex \lambda\$ is the wavelength of the wave
$x$ is the distance between the $n_{0}$ and $n_{1 }$ fringes
$a$ is the slit separation
$D$ is the distance between the slits and the screen

Page co-written with Luca Quinci – Thank you!