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°.
