Question

Light of wavelength 645 nm is incident on a double slit. The angle between the central bright fringe and the second dark fringe is 4.90°. Determine the separation d of the slits.

Answer 1

Answer:

Slit separation, $d=1.13\times 10^{-5}\ m$

Explanation:

It is given that,

Wavelength of light, $\lambda=645\ nm=645\times 10^{-9}\ m$

The angle between the central bright fringe and the second dark fringe, $\theta=4.9^{\circ}$

In case of double slits, the condition for dark fringe is given by :

$d\ sin\theta=(n-\dfrac{1}{2})\lambda$

n = 2

$d\ sin\theta=\dfrac{3}{2}\lambda$

$d=\dfrac{3\lambda}{2\ sin\theta}$

$d=\dfrac{3\times 645\times 10^{-9}}{2\ sin(4.9)}$

$d=1.13\times 10^{-5}\ m$

So, the slit separation is $1.13\times 10^{-5}\ m$. Hence, this is the required solution.