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

Wavelength of light used is 387 nm.

Step-by-step 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=(1)/(N)=(1)/(390000)`

`d=2.56* 10^(-6)\ m`

`\lambda=(d\ sin\theta)/(n)`

`\lambda=(2.56* 10^(-6)* \ sin(27))/(3)`

`\lambda=3.87* 10^(-7)\ m`

`\lambda=387\ nm`

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