Question

A single, monochromatic indigo light source is shined through an etched, flat prism with a slit separation of .0250mm. The resulting interference pattern is viewed on a screen 1.25m away. The third maximum is found to be 6.6cm from the central maximum. What is the wavelength of the indigo light

Answer 1

λ = 440 nm

Step-by-step explanation:

The phenomenon of constructive interference is described by the expressions

d sin θ= m λ (1)

where d is the separation of the slits d = 0.0250 mm = 2.50 10⁻⁵ m, lam is the wavelength of the incident radiation and m is an integer indicating the order of interference

let's use trigonometry to find the angle

tan θ = y / L

where L is the distance to the screen L = 1.25 m

in general interference experiments angles are very small

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

ten θ = sin θ

substituting

sin θ = y / L

we substitute 1

d y / L = m λ

λ =
`( d \ y )/(m \ L)`

in the exercise indicate

m = 3

y = 6.6 cm = 6.6 10-2 m

we calculate

λ = 2.50 10⁻⁵ 6.6 10⁻² /( 3 1.25)

λ = 4.4 10⁻⁷ m

let's reduce to nm

λ = 4.4 10⁻⁷ m (10⁹ nm / 1 m)

λ = 440 nm