Question

Two slits separated by 0.425 mm are illuminated with light of an unknown wavelength and an interference pattern is observed on a screen 3.13 m away. The tenth bright line is 49.1 mm from the central maximum. The wavelength of the light is nm?

Answer 1

wavelength is 666.6933 ×
`10^(-9)` m

Step-by-step explanation:

given data

Two slits separated d = 0.425 mm

screen away D = 3.13 m

tenth bright line (y) = 49.1 mm

to find out

The wavelength of the light

solution

let angle θ at which bright fringed occurs

so that

tanθ = y / D

here D id slits to screen distance and tanθ = θ

and

construction interference equation

sinθ = m β / d

and here sinθ = θ and β is wavelength

θ = m β / d

and

θ = m β / d

y / D = m β / d

β = y d / Dm

wavelength = 49.1
`10^(-3)` × 0.425
`10^(-3)` / 3.13 (10)

wavelength = 49.1
`10^(-3)` × 0.425
`10^(-3)` / 3.13 (10)

wavelength is 666.6933 ×
`10^(-9)` m