Question

A grating that has 3900 slits per cm produces a third-order fringe at a 27.0° angle. What wavelength of light is being used?

Answer 1

Answer:

Wavelength of light used is 387 nm.

Explanation:

It is given that,

Number of lines, N = 3900 slits per cm

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

Third order fringe is formed at angle of, $\theta=27^{\circ}$

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

$d\ sin\theta=n\lambda$, n = 3

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

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

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

$\lambda=\dfrac{2.56\times 10^{-6}\times \ sin(27)}{3}$

$\lambda=3.87\times 10^{-7}\ m$

$\lambda=387\ nm$

So, the wavelength of light used is 387 nm. Hence, this is the required solution.