Question

A slit of width d is illuminated by red light of wavelength λ=6500 angstroms. For what value of d does the first minima fall?

a) 3250 angstroms
b) 6500 angstroms
c) 13000 angstroms
d) 19500 angstroms

Answer 1

To find the slit width where the first minima falls in a diffraction pattern for red light with a wavelength of 6500 angstroms, we use d = λ, resulting in a slit width of 6500 angstroms.

Step-by-step explanation:

The question relates to the diffraction pattern of light as it passes through a single slit, which is an important concept in wave optics. The equation used to find the position of minima in a diffraction pattern is given as d sin θ = mλ, where d is the slit width, θ is the diffraction angle, m is the order of the minimum, and λ is the wavelength of light. For the first minimum (m = 1), this equation simplifies to d sin θ = λ. If we are looking for the slit width that causes the first minimum to occur when illuminated by red light with a wavelength λ = 6500 angstroms, we use the simplified equation knowing that for the first minimum, the angle θ is such that sin θ = 1. This results in the relationship d = λ, hence d also equals 6500 angstroms.