Question

In the two-slit experiment, monochromatic light of frequency 5.00 × 1014 Hz passes through a pair of slits separated by 2.20 × 10-5 m. (c = 3.00 × 108 m/s) (a) At what angle away from the central bright spot does the third bright fringe past the central bright spot occur?

Answer 1

Answer:

$\theta=4.64^{\circ}$

Explanation:

It is given that,

The frequency of monochromatic light, $f=5\times 10^{14}\ Hz$

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

Let $\theta$ is the angle away from the central bright spot the third bright fringe past the central bright spot occur. The condition for bright fringe is :

$d\ sin\theta=n\lambda$

n = 3

$\lambda=\dfrac{c}{f}$

$d\ sin\theta=\dfrac{nc}{f}$        

$sin\theta=\dfrac{nc}{fd}$        

$sin\theta=\dfrac{3\times 3\times 10^8}{5\times 10^{14}\times 2.2\times 10^{-5}}$  

$\theta=4.64^{\circ}$

So, at 4.64 degrees the third bright fringe past the central bright spot occur. Hence, this is the required solution.