Question

Light of wavelength 520 nm passes through two narrow slits 0.66 mm apart. The screen is 1.60 m away. A second source of unknown wavelength produces its second-order fringe 1.23 mm closer to the central maximum than the 520 nm light. What is the wavelength of the unknown light

Answer 1

λ = 266 nm

Step-by-step explanation:

In this case, we need to determine first the separation of the second fringe from the central maximum. We can determine that with the following expression:

d sinθ = mλ (1)

However, as the slits are very narrow, we can assume that sin θ ≈ θ and so θ = x/l

Replacing this in (1) we have:

d(x/l) = mλ

and solving for x:

x = mλl / d (2)

Where:

x: separation of the 2nd fringe from the central maximum

m: order of the fringe

λ: wavelength of light

l: distance of the screen

d: distance between the slits

All the units must be in meters (m), so we can convert the units first or during the resolution. In this case, we'll do it in the resolution. Replacing the given data, we have:

x = 2 * (520 nm * 1m/10⁻⁹ nm) * 1.6 m / (0.66 mm * 1m/1000 mm)

x = 0.00252 m or just 2.52 mm

With this value, we can compute or determine the separation of the 2nd order fringe of the unknown light in the central maximum:

x₂ = 2.52 - 1.23 = 1.29 mm or 0.00129 m

Now, using (2) we can solve for λ:

λ = dx / ml (3)

Replacing we have:

λ = (0.00129 * 0.0066) / (2 * 1.6)

λ = 2.66x10⁻⁷ m or simply 266 nm

Hope this helps