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?

Question

asked Apr 24, 2020 77.3k views

1 Answer

Thewebjackal · Answer 1 · 2020-04-28T22:39:21+0000

Step-by-step explanation:

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

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

Where:

is the width of the slit

$\lambda$ is the wavelength of the light

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.