Question

 

Young's experiment is performed with light of wavelength 502nm from excited helium atoms. Fringes are measured carefully on a screen 1.35m away from the double slit, and the center of the 20th fringe (not counting the central bright fringe) is found to be 10.4mm from the center of the central bright fringe.

 

What is the separation of the two slits?

Answer 1

Concepts and reason

The concept required to solve the given question is slit width in the Young’s experiment.

Initially, convert the wavelength form nm to m. Finally, calculate the separation of the two slits by rearranging the equation obtained from the Young’s double slit experiment.

Fundamentals

The expression for the Young’s double slit experiment is as follows:

$n\lambda = \frac{{Yd}}{D}$

Here, n is the order of diffraction, d is the separation of the two slits, D is the distance from the slits to the screen, $\lambda$ is the wavelength, Y is the distance of the fringe from the central bright fringe.

The wavelength in nm is as follows:

$\lambda = 502{\rm{ nm}}$

Convert the wavelength in m as follows:

$\begin{array}{c}\\\lambda = \left( {502{\rm{ nm}}} \right)\left( {\frac{{{{10}^{ - 9}}{\rm{ m}}}}{{1.00{\rm{ nm}}}}} \right)\\\\ = 502 \times {10^{ - 9}}{\rm{ m}}\\\end{array}$

Rearrange the equation $n\lambda = \frac{{Yd}}{D}$ for d as follows:

$d = \frac{{n\lambda D}}{Y}$

Substitute 20 for n, $502 \times {10^{ - 9}}{\rm{ m}}$ for $\lambda$ , 10.4 mm for Y, and 1.35 m for D in the equation $d = \frac{{n\lambda D}}{Y}$ .

$\begin{array}{c}\\d = \frac{{\left( {20} \right)\left( {502 \times {{10}^{ - 9}}{\rm{ m}}} \right)\left( {1.35{\rm{ mm}}} \right)}}{{\left( {10.4{\rm{ mm}}} \right)}}\\\\ = \frac{{\left( {20} \right)\left( {502 \times {{10}^{ - 9}}{\rm{ m}}} \right)\left( {1.35{\rm{ mm}}} \right)}}{{\left( {10.4{\rm{ mm}}} \right)}}\\\\ = \left( {1.30 \times {{10}^{ - 6}}{\rm{ m}}} \right)\left( {\frac{{{{10}^6}{\rm{ mm}}}}{{1{\rm{ m}}}}} \right)\\\\{\rm{ = }}1.30{\rm{ mm}}\\\end{array}$

Ans:

The magnitude of the separation of the two slits is 1.30 mm.