In a single slit diffraction experiment, the width of the central maxima is given by the diffraction pattern formula derived from the Huygens-Fresnel principle. The position of the first minima in the diffraction pattern is given by:
asin(θ)=nλwhere
a is the slit width,
θ is the angle of the diffraction minimum,
n is the order of the minimum (for the first minimum,
n=1 ), and
λ is the wavelength of the light used.
The angular width of the central maxima is approximately twice the angle to the first minimum:
∆θ= When projecting this onto a screen at a distance
D, the width of the central maximum car be approximated by:
β=2Dtan(θ)≈2D()If the slit width
a is doubled, say to
2a, then the new width of the central maximum
β′ becomes:
β′=2D()=Thus, if the slit width is doubled, the corresponding width of the central maxima will be: Option C:
.