Final answer:
The angular width of the principal maximum in a single slit diffraction pattern is approximately 2λ/d, where d is the width of the slit and λ is the wavelength of the light.
option a is the correct
Step-by-step explanation:
The student's question addresses the phenomenon known as single slit diffraction, which pertains to Physics. In a single slit diffraction pattern, the angular width of the principal maximum is determined by the width of the slit and the wavelength of the light used. According to the principles of wave optics, when a wavefront of light encounters a narrow slit, it diffracts and spreads out, creating a pattern on a screen.
The central maximum is the brightest and also the broadest part of the diffraction pattern, and its angular width can be found using the formula for the position of the minima, which is given by D sin θ = mλ, where D is the width of the slit, θ is the angle of the diffraction minimum, λ is the wavelength of the light, and m is the order of the minimum. For the first minimum (m=1), this translates to θ = arcsin(λ/D). Therefore, the angular width of the central maximum is twice this value since it extends from the negative first-order minimum to the positive first-order minimum. Hence the angular width of the principal maximum is approximately 2λ/d, which corresponds to choice A in the student's multiple-choice question.