Question

A diffraction grating with 750 slits per mm is illuminated by light which gives a first-order diffraction angle of 34.0°. What is the wavelength of the light?

Answer 1

Answer: 745.59 nm

Step-by-step explanation:

The diffraction angles
`\theta_(n)` when we have a slit divided into
`n` parts are obtained by the following equation:

`dsin\theta_(n)=n\lambda` (1)

Where:

`d` is the width of the slit

`\lambda` is the wavelength of the light

`n` is an integer different from zero

Now, the first-order diffraction angle is given when
`n=1`, hence equation (1) becomes:

`dsin\theta_(1)=\lambda` (2)

We know:

`\theta_(1)=34\°`

In addition we are told the diffraction grating has 750 slits per mm, this means:

`d=(1mm)/(750)`

Solving (2) with the known values we will find
`\lambda`:

`\lambda=((1mm)/(750))sin(34\°)` (3)

`\lambda=0.00074559mm` (4)

Knowing
`1mm=10^(6)nm`:

`\lambda=745.59nm` >>>This is the wavelength of the light, wich corresponds to red.