Question

A diffraction grating has 755 slits/mm. What is the highest order that contains the entire visible spectrum? (The wavelength range of the visible spectrum is approximately 400-700 nm.)

Answer 1

The maximum diffraction of the grating is -

d*sine theta = m*lemda

where, m = 0, 1, 2, 3, 4, ......

Now, given that the diffraction grating has 755 slits/mm.

So, d = 1/(755 slits/mm) = 1.32 x 10^-6 m.

From the above expression -

sine theta = m*lemda / d

and this should be less than or equal to 1 for all wavelengths to be seen.

for m = 1

sine theta = (1*700 x 10^-9) /(1.32 x 10^-6) = 0.53

for m = 2

sine theta = (2*700 x 10^-9) /(1.32 x 10^-6) = 1.06

And this is not possible.

Therefore, the highest order that contains the visible spectrum is, m = 1.