Question

Calculate the wavelength of light that has its third minimum at an angle of 30.0º when falling on double slits separated by 3.00 µm.

Answer 1

λ = 428.6 nm

Step-by-step explanation:

Hello,

In this case, we must remember that the Young's double slit experiment is described by the expression :

d sin θ = m λ

For constructive interference , and:

d sin θ = (m + ½) λ

For destructive interference , whereas d accounts for the distance between the slits, λ for the wavelength and m for an integer that describes the order of interference . Thus, for the given angle 30º, the distance between the slits is 3.00 μm or 3.00 10⁻⁶ m and the order of interference is 3; we therefore use the destructive interference equation to compute the wavelength as shown below:

λ = 3x10⁻⁶ sin (30) / (3 +1/2)

λ = 4.286 10⁻⁷ m

Or in manometers:

λ = 428.6 nm

Best regards.