Question

Light shines through a single slit whose width is 5.7 × 10-4 m. A diffraction pattern is formed on a flat screen located 4.0 m away. The distance between the middle of the central bright fringe and the first dark fringe is 4.2 mm. What is the wavelength of the light?

Answer 1

Explanation:

It is given that,

Slit width, $d=5.7\times 10^{-4}\ m$

A diffraction pattern is formed on a flat screen located 4.0 m away, L = 4 m

The distance between the middle of the central bright fringe and the first dark fringe is 4.2 mm, y = 4.2 mm = 0.0042 m

Let $\lambda$ is the wavelength of the light.

Using condition of diffraction as,

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

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

Also, $tan\theta=\dfrac{y}{L}$

$\theta=tan^{-1}(\dfrac{y}{L})=tan^{-1}(\dfrac{0.0042}{4})=0.060$

$\lambda=\dfrac{5.7\times 10^{-4}\ sin(0.060)}{1}$

$\lambda=596\ nm$

So, the wavelength of the light is 596 nm. Hence, this is the required solution.