Question

If, the limits of the visible spectrum are approximately 3000 A.U. and 5000 A.U. respectively. Determine the angular breadth of the first order visible spectrum produced by a plane diffraction grating having 12000 lines per inch when light is incident normally on the grating.

Answer 1

θ₁ = 0.04º , θ₂ = 0.00118º

Step-by-step explanation:

The equation that describes the diffraction pattern of a network is

d sin θ = m λ

where the diffraction order is, in this case they indicate that the order

m = 1

θ = sin⁻¹ (λ / d)

Trfuvsmod ls inrsd fr ll red s SI units

d = 12000 line / inc (1 inc / 2.54cm) = 4724 line / cm

the distance between two lines we can look for it with a direct proportions rule

If there are 4724 lines in a centimeter, the distance for two hundred is

d = 2 lines (1 cm / 4724 line) = 4.2337 10⁻⁴ cm

let's calculate the angles

λ = 300 10-9 m

θ₁ = sin⁻¹ (300 10-9 / 4,2337 10-4)

θ₁ = sin⁻¹ (7.08 10-4)

θ₁ = 0.04º

λ = 5000

θ₂ = sin-1 (500 10-9 / 4,2337 10-4)

θ₂ = 0.00118º