Final answer:
The angle at which a 2.00-μm-wide slit produces its first minimum for 410-nm violet light is 34.12 degrees.
Step-by-step explanation:
To calculate the angle at which a 2.00-μm-wide slit produces its first minimum for 410-nm violet light, we can use the equation for single-slit diffraction:
θ = sin^(-1)((mλ)/w)
where θ is the angle, m is the order of the minimum (for the first minimum, m = 1), λ is the wavelength of the light, and w is the width of the slit.
Plugging in the values for the violet light with λ = 410 nm and w = 2.00 μm, we get:
θ = sin^(-1)((1 * 410 * 10^(-9))/(2 * 10^(-6)))
θ = 34.12 degrees