Question

Light falls on two slits 0.0000716 m apart and produces an interference pattern in which

the fourth-order fringe is 0.038 m from the central fringe on a screen 1.0 m away.
A) What is the wavelength of the light?
B) Roughly what color is the light?

Answer 1

λ = 6.802 10⁻⁷ m, wavelength corresponds to orange almost red

Step-by-step explanation:

The expression for constructive interference is

d sin θ = m λ

let's use trigonometry

tan θ = y / L

tan θ = sin θ / cos θ

interference experiments angles are very small

tan θ = sin θ = y / L

substituting

`d \ (y)/(L)` = m λ

in this case they indicate the separation of the slits d = 7.16 10-5 m, the order of the interference is m = 4, the distance y = 3.8 10-2 m and the separation to the screen L = 1 m

A) they ask us for the wavelength

λ =
`(d y)/( m L)`

let's calculate

λ = 7.16 10⁻⁵ 3.8 10⁻² /(4 1)

λ = 6.802 10⁻⁷ m

B) Let's reduce the wavelength to nm

λ = 6.802 10⁻⁷ m (109 nm / 1m)

λ = 680.2 nm

this wavelength corresponds to orange almost red