Question

In a Young’s double-slit experiment, the angle that locates the second dark fringe on either side of the central bright fringe is 5.4. Find the ratio d/ of the slit separation d to the wavelength of the light. (d / λ) =?

Answer 1

In a Young's double-slit experiment, the ratio of the slit separation d to the wavelength λ can be determined using the formula d/λ = 1/(sinθ), where θ is the angle that locates the fringe. In this case, the angle is given as 5.4°, so we can substitute it into the formula to find the ratio d/λ.

Step-by-step explanation:

In a Young's double-slit experiment, the angle that locates the second dark fringe on either side of the central bright fringe is 5.4°. We can use the formula dsinθ = nλ, where d is the slit separation, θ is the angle, n is the order of the fringe, and λ is the wavelength of the light. Here, n = 1 for the second dark fringe. Since sinθ is small (sin ≈ θ for small angles), we can use the approximation Δy = xλ/d, where Δy is the distance between fringes, x is the distance from the double slit to the screen, λ is the wavelength, and d is the slit separation.

So, using the given value of θ = 5.4° and n = 1, we have dsinθ = nλ. Rearranging the equation to get d/λ, we have d/λ = 1/(sinθ). Substitute θ = 5.4° to find the ratio d/λ.

Answer 2

d / λ = 26.7

Step-by-step explanation:

In Young's double slit experiment, constructive interference is described by the expression

d sin θ = m λ

In the case of destructive interference we must add half wavelength (λ/2)

d siyn θ = (m + ½) λ

Let's clear

d / λ = (m + ½) / sin θ

Let's calculate

d / λ = (2+ ½) / sin 5.4

d / λ = 5 / (2 sin 5.4)

d / λ = 26.7