Adiffraction 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?

Explanation:

The diffraction angles when we have a slit divided into parts are obtained by the following equation:

(1)

Where:

is the width of the slit

is the wavelength of the light  

is an integer different from zero

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

(2)

We know:

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

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

(3)

(4)

Knowing :

 >>>This is the wavelength of the light, wich corresponds to red.

d.7.5cm is your answer