Question

A grating that has 3900 slits per cm produces a third- order fringe at a 28.0° angle. What wavelength of light is being used? Express your answer to two significant figures and include the appropriate units.

Answer 1

Explanation:

Given that,

Number of slits per cm, $N=3900\ lines/cm=390000\lines/m$

The third fringe is obtained at an angle of, $\theta=28$

We need to find the wavelength of light used. The grating equation is given by :

$d\ sin\theta=n\lambda$

$d=\dfrac{1}{N}=\dfrac{1}{390000}$

$d=2.56\times 10^{-6}\ m$

$\lambda=\dfrac{d\ sin\theta}{n}$, n = 3

$\lambda=\dfrac{2.56\times 10^{-6}\times \ sin(28)}{3}$

$\lambda=4.006\times 10^{-7}\ m$

$\lambda=400\ nm$

So, the wavelength of the light is 400 nm. Hence, this is the required solution.