Question

The two most prominent wavelengths in the light emitted by a hydrogen discharge lamp are 656 nm (red) and 486 nm (blue). Light from a hydrogen lamp illuminates a diffraction grating with 550 lines/mm , and the light is observed on a screen 1.7 m behind the grating.

What is the distance between the first-order red and blue fringes?
Express your answer to two significant figures and include the appropriate units.

Answer 1

Δd = 7.22 10⁻² m

Step-by-step explanation:

For this exercise we must use the dispersion relationship of a diffraction grating

d sin θ = m λ

let's use trigonometry

tan θ = y / L

how the angles are small

tant θ = sinθ /cos θ = sin θ

we substitute

sin θ = y / L

d y / L = m λ

y = m λ L / d

let's use direct ruler rule to find the distance between two slits

If there are 500 lines in 1 me, what distance is there between two lines

d = 2/500

d = 0.004 me = 4 10⁻⁶ m

diffraction gratings are built so that most of the energy is in the first order of diffraction m = 1

let's calculate for each wavelength

λ = 656 nm = 656 10⁻⁹ m

d₁ = 1 656 10⁻⁹ 1.7 / 4 10⁻⁶

d₁ = 2.788 10⁻¹ m

λ = 486 nm = 486 10⁻⁹ m

d₂ = 1 486 10⁻⁹ 1.7 / 4 10⁻⁶

d₂ = 2.066 10⁻¹ m

the distance between the two lines is

Δd = d1 -d2

Δd = (2,788 - 2,066) 10⁻¹

Δd = 7.22 10⁻² m