Question

A parallel beam of light falls on two small slits 5x10-5 m apart.

A) If the distance between the central and 1st fringe is 0.06 m and the light is being
projected onto a screen 5 m away, what is the wavelength of the light?
B) Roughly what color is it?

Answer 1

λ = 6 10⁻⁷ m, color orange

Step-by-step explanation:

This problem is about the interference phenomenon, constructive interference occurs when the path difference is equal to an integer number of wavelengths

d sim θ = m λ

Let's use trigonometry, remembering that the angles for these experiments are very small.

Sin θ = y / L

tan θ =
`(sin \theta)/(cos \theta)` = sin θ

sin θ = y / L

we substitute

`d \ (y)/(L) = m \lambda`

A) Donut length is requested

λ =
`(d \ y)/(m \ L)`

let's calculate

λ = 5 10⁻⁵ 0.06 /( 1 5)

λ = 6 10⁻⁷ m

B) let's express the wavelength in nm

λ = 6 10⁻⁷ m = 600 nm

this corresponds to the color orange