Question

Red laser light from a He-Ne laser (λ = 632.8 nm) creates a second-order fringe at 53.2° after passing through the grating. What is the wavelength λ of light that creates a first-order fringe at 22.0°?

Answer 1

Step-by-step explanation:

It is given that,

Wavelength of red laser light,
`\lambda=632.8\ nm=632.8* 10^(-9)\ m`

The second order fringe is formed at an angle of,
`\theta=53.2^(\circ)`

For diffraction grating,

`d\ sin\theta=n\lambda`

`d=(n\lambda)/(sin\theta)`, n = 2

`d=(2* 632.8* 10^(-9))/(sin(53.2))`

`d=1.58* 10^(-6)\ m`

The wavelength λ of light that creates a first-order fringe at 22 is given by :

`\lambda=d\ sin\theta`

`\lambda=1.58* 10^(-6)\ sin(22)`

`\lambda=5.91* 10^(-7)\ m`

`\lambda=591\ nm`

Hence, this is the required solution.