Question

Q 3. (a) A diffraction grating used at normal incidence gives a line 5400 A in
superimposed another line 4050Âof the next higher order. If the angle of diffraction is 30°, how
many lines/cm are there on grating?

Answer 1

Given info : A diffraction grating used at normal incidence gives a line 5400 A in superimposed another line 4050A° of the next higher order. If the angle of diffraction is 30°.

To find : number of lines per cm are there on grating.

Solution : using formula, (a + b)sinθ = nλ

For 1st case,

(a + b)sin30° = n × 5400 A°.......(1)

For 2nd case,

(a + b)sin30° = (n + 1) × 4050 A° ......(2)

From equations (1) and (2) we get,

n/(n + 1) = 4050/5400

⇒ n/(n + 1) = 405/540 = 81/108 = 3/4

⇒4n = 3n + 3

⇒n = 3

Therefore 4 lines or cm are there on the grating.