Final answer:
To calculate the wavelength of light with the third minimum at an angle of 48.6° on a 3.00µm single slit, we use the diffraction equation and solve for the wavelength. The closest match to the calculated wavelength of 720 nm from the options provided is 800 nm. So, the correct option is D.
Step-by-step explanation:
To find the wavelength of light that has its third minimum at an angle of 48.6° when it falls on a single slit of width 3.00µm, we can use the diffraction minima condition for a single slit, which is given by:
mλ = a sin(θ)
Where m is the order number of the minimum, λ is the wavelength, a is the slit width, and θ is the angle of the minimum.
For the third minimum (m = 3), the angle given is θ = 48.6° and the slit width a = 3.00µm. To find the wavelength (λ), we rearrange the equation as follows:
λ = (a sin(θ)) / m
Now, plugging in the values we get:
λ = (3.00 × 10^-6 m × sin(48.6°)) / 3
Calculating this, we find that λ = 7.20 × 10^-7 m or 720 nm. However, we must look at the options given to find the closest match. Therefore, the answer is:
d) 800 nm