Final answer:
To find the wavelength of light for the third minimum at an angle of 30º in a double-slit interference pattern, we use the formula mλ = d·sin(θ), which yields a wavelength of 500 nm for light when slit separation is 3.00 μm.
Step-by-step explanation:
To 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, we use the formula for minima in a double-slit interference pattern:
mλ = d·sin(θ)
where m is the order of the minimum, λ is the wavelength of light, d is the separation between the slits, and θ is the angle of the minimum.
For the third minimum (m=3), the angle θ is given as 30.0º, and the slit separation d is 3.00 μm. Plugging in the values we have:
3λ = (3.00 μm)·sin(30.0º)
Solving for λ, we get:
λ = (3.00 μm)·sin(30.0º) / 3
Since sin(30.0º) is 0.5, the equation simplifies to:
λ = (3.00 μm)·(0.5) / 3
λ = (1.50 μm) / 3
λ = 0.50 μm = 500 nm
The wavelength of the light is therefore 500 nm.