In Young's experiment a mixture of orange light (611 nm) and blue light (471 nm) shines on the double slit. The centers of the first-order bright blue fringes lie at the outer edges of a screen that is located 0.423 m away from the slits. However, the first-order bright orange fringes fall off the screen. By how much and in what direction (toward or away from the slits) should the screen be moved, so that the centers of the first-order bright orange fringes just appear on the screen? It may be assumed that is small, so that sin is approximately equal to tan , and the sign ''+'' means that the screen moves toward the slits.

Question

In Young's experiment a mixture of orange light (611 nm) and blue light (471 nm) shines on the double slit. The centers of the first-order bright blue fringes lie at the outer edges of a screen that is located 0.423 m away from the slits. However, the first-order bright orange fringes fall off the screen. By how much and in what direction (toward or away from the slits) should the screen be moved, so that the centers of the first-order bright orange fringes just appear on the screen? It may be assumed that is small, so that sin is approximately equal to tan , and the sign ''+'' means that the screen moves toward the slits.

Answer 1

To find the required shift of the screen in order to bring the centers of the first-order bright orange fringes onto the screen, we can use the formula for fringe spacing in Young's double-slit experiment.

The formula for fringe spacing is given by:

dλ = y * λ / D

where:
dλ is the fringe spacing (distance between adjacent bright fringes),
y is the distance on the screen from the central maximum to the desired fringe,
λ is the wavelength of light,
D is the distance between the double slits and the screen.

In this case, we want to find the shift of the screen required to bring the bright orange fringes onto the screen. Since the first-order bright blue fringes already fall on the screen, we can use the distance between the first-order bright blue fringes as the fringe spacing for both colors.

Let's assume that the shift of the screen required to bring the bright orange fringes onto the screen is Δy. Therefore, the distance from the central maximum to the desired orange fringe would be (y - Δy).

Using the formula for fringe spacing, we can set up the following equation:

dλ_orange = (y - Δy) * λ_orange / D

Since we know that sin(θ) ≈ tan(θ) for small angles, and the fringe spacing is inversely proportional to the distance between the screen and the double slits, we can approximate the fringe spacings as follows:

dλ_orange = (y - Δy) * λ_orange / D ≈ y * λ_orange / (D + ΔD)

Simplifying the equation further:

(y - Δy) * λ_orange ≈ y * λ_orange + y * λ_orange * ΔD / D

Canceling out the common terms:

-y * Δy * λ_orange ≈ y * λ_orange * ΔD / D

Simplifying and solving for Δy:

Δy ≈ ΔD * y / D

Since ΔD is the required shift of the screen, Δy represents the shift of the orange fringes in the same direction. Therefore, the sign "+" in the problem statement refers to the screen moving toward the slits.

Hence, the screen should be moved by a small distance of Δy towards the double slits in order to bring the centers of the first-order bright orange fringes onto the screen.