. The yellow light from a helium discharge tube has a wavelength of 587.5 nm. When this light illuminates a certain diffraction grating it produces a second-order principal maximum at an angle of 1.170°. Calculate the number of lines per centimeter on the grating.

344.8 lines/cm

Explanation:

Given

Wavelength of the light, λ = 587.5 nm

Angle, θ = 1.17°

To solve, we use the formula

Wsin θ = mλ, where m is first order, so m = 1

Converting the nm to cm, we have 587.5*10^9 * 100 = 587.5 * 10^-7 cm

So, taking mλ/sin θ = W

(1)(587.5*10^-7 cm) / sin1.17° = W

W = 587.5*10^-7 cm / 0.020

W = 0.0029

But since it has to be in lines/cm, so take the inverse:

1 / 0.0029 cm

= 344.8 lines/cm

Therefore, the lines/cm on the grating is 344.8 lines/cm