The human eye can readily detect wavelengths from about 400 nm to 700 nm. if white light illuminates a diffraction grating having 750 lines/mm, over what range of angles does the visible m = 1 spectrum extend?

The range of angles is from 17.50° to 31.76°

Explanation:

The diffraction grid equation is as follows:

Clearing for

where is the angle, is the order, in this case , is the wavelength, and is defined as follows:

and since the resolution is 750 lines/mm wich is the same as

will be:

wich is the distance between each line of the diffraction grating.

substituting the values for and :

And we need to find two angle values: one for when the wavelength is 400nm and one for when it is 700 nm. So we will get the angle range

and

The range of angles is from 17.50° to 31.76°

0 = 0.40 / 0 = 0

= 0.20 = 9.80 ⁄2 =?

=0 , = = 0.20 =0.50 0 0.40 ⁄

=0−122 =0−12(9.80 ⁄2)(0.50)2 =1.2