Light of wavelength 600nm illuminates a diffraction grating. The second-order maximum is at angle 39°. How many lines per millimeter does this grating have?

the number of lines is 526

Explanation:

The wavelength  λ =600nm = 600 × 10⁻⁶ mm

The diffraction angle θ = 39°

Recall the expression for the relation between the wavelength, angle and central maxima distance.

Recall the expression for the relation between the wavelength, angle and central maxima distance.

Recall the expression for the relation between the wavelength, angle and central maxima distance.

relation between the wave length, angle and central maxima distance

d =  nλ / sinθ

Here n = 2 for second order maxima and d is the distance

= 2(600 × 10⁻⁶) / sin 39°

= 1200 × 10⁻⁶ / 0.6293

= 1.9 × 10⁻³ mm

N = 1/d

= 1 / 1.9 × 10⁻³

= 526

The grating has a line density of 526 lines per millimeter