Final answer:
The formula for destructive interference in diffraction grating problems is dsin θ = (n + 1/2)λ, where d is the spacing between the slits or lines on the diffraction grating, θ is the angle of incidence, n is the order of the interference, and λ is the wavelength of light.
Step-by-step explanation:
The formula for destructive interference in diffraction grating problems is dsin θ = (n + 1/2)λ, where d is the spacing between the slits or lines on the diffraction grating, θ is the angle of incidence, n is the order of the interference, and λ is the wavelength of light.
This formula represents the constructive interference condition for a diffraction grating, where the path difference between the light waves from adjacent slits or lines is equal to an odd integral multiple of the wavelength.
For example, if the diffraction grating has a slit spacing of 1.0 mm, and the wavelength of light is 500 nm (0.5 μm), and we want to find the angle at which destructive interference occurs for the first-order (n = 1) diffraction, we can use the formula as follows:
dsin θ = (n + 1/2)λ
1.0 mm * sin θ = (1 + 1/2) * 0.5 μm
sin θ = 0.75