Question

In a Young's double-slit experiment, the slits are separated by $0.28mm$ and the screen is placed $1.4m$ away. The distance between the central bright fringe and the fourth bright fringe is measured to be $1.2cm$. Determine the wavelength of light used in the experiment.

Answer 1

Hint : The distance between successive crests in a sound wave is called wavelength. Young's double slit experiment demonstrated that light and matter can display characteristics of waves and particles and it displays the nature of quantum mechanical phenomena.

Complete step by step solution:
For constructive interference the distance between two fringes can be found out as
$u = \dfrac{{n\lambda D}}{d}$
Where d is the distance between the slits
D is distance between slit and screen
U is the distance between central fringe and fourth fringe
$\lambda$ is the wavelength of the light used.
The given values are
$d = 0.28mm \\\ \Rightarrow d = 0.28 \times {10^{ - 3}}m \\\ D = 1.4m \\\ n = 4 \\\ u = 1.2cm \\\ \Rightarrow u = 1.2 \times {10^{ - 2}}m \\\$
Substituting the values in the equation we get,
$\lambda = \dfrac{{ud}}{{nD}} \\\ \Rightarrow \lambda = \dfrac{{1.2 \times {{10}^{ - 2}} \times 0.28 \times {{10}^{ - 3}}}}{{4 \times 1.4}} \\\ \Rightarrow \lambda = 6 \times {10^{ - 7}}m \\\ \Rightarrow \lambda = 600nm \\\$

So, the wavelength of the light used in the experiment is $600nm$

Additional Information:
There are two types of interference: constructive and destructive interference.
If the amplitude of the waves is increasing due to lining up of their crest then it is called constructive interference resulting in waves of higher amplitude and in destructive interferences the crest of one wave meets the trough of one another and results in lowering of amplitude.

Note:
Conditions for constructive interference is that phase difference between the waves should be an even integral multiple of $\pi {\text{ or 18}}{{\text{0}}^ \circ }$.
Conditions for destructive interference is that phase difference between the waves should be an odd integral multiple of $\pi {\text{ or 18}}{{\text{0}}^ \circ }$.