Answer:
The angular width of the central peak is 24.2 degrees
Explanation:
The equation that describes the single-slit diffraction phenomenon is:
[tex] a\sin\theta=m\lambda [/tex] (1)
with a the width of the slit, [tex]\theta [/tex] the angular position of the minimum regarding the center of the screen where light is projected, m the order of the minimum and [tex] \lambda [/tex] the wavelength. Solving (1) for [tex] \theta [/tex] with m=1 that is the first minimum:
[tex]\theta=\arcsin(\frac{m\lambda}{a})=\arcsin(\frac{(1)(633\times10^{-9})}{3.0\times10^{-6}})\approx12.1 deg [/tex]
See the figure below that the central peak is symmetric regarding the center of the screen, which implies that the angular width of the central peak is [tex] 2\theta =2(12.1 deg) = 24.2 deg[/tex]
