Question

In the two-slit experiment, monochromatic light of wavelength 600 nm passes through a 19) pair of slits separated by 2.20 x 10-5 m. (a) What is the angle corresponding to the first bright fringe? (b) What is the angle corresponding to the second dark fringe?

Answer 1

Explanation:

It is given that,

Wavelength of monochromatic light, $\lambda=600\ nm=6\times 10^{-7}\ m$

Slits separation, $d=2.2\times 10^{-5}\ m$

(a) We need to find the angle corresponding to the first bright fringe. For bright fringe the equation is given as :

$d\ sin\theta=n\lambda$, n = 1

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

$\theta=sin^{-1}(\dfrac{6\times 10^{-7}}{2.2\times 10^{-5}})$

$\theta=1.56^{\circ}$

(b) We need to find the angle corresponding to the second dark fringe, n = 1

So, $d\ sin\theta=(n+\dfrac{1}{2})\lambda$

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

$\theta=sin^{-1}(\dfrac{3\lambda}{2d})$

$\theta=sin^{-1}(\dfrac{3\times 6\times 10^{-7}}{2\times 2.2\times 10^{-5}})$

$\theta=2.34^{\circ}$

Hence, this is the required solution.