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

We are given that the wavelength ʎ is from 400 nm to 700 nm. The formula for this is:

d sin a = m * ʎ

where,

d = slit separation = 1 mm / 750 lines = 1/750

a = angle

m = 1

ʎ = 400 nm to 700 nm = 0.0004 mm to 0.0007 mm

Rewriting the formula in terms of angle a:

a = sin^-1 (m ʎ / d)

when ʎ = 0.0004 mm

a = sin^-1 (0.0004 / (1/750))

a = 17.46°

when ʎ = 0.0007 mm

a = sin^-1 (0.0007 / (1/750))

a = 31.67°

Hence the range of angles is from 17.46° to 31.67 °.