Answer:
The angular resolution is 0.0146°
Explanation:
Given:
Diameter of pupil eye [tex]a = 8 \times 10^{-3}[/tex] m
Diameter of pupil eye [tex]a' = 2 \times 10^{-3}[/tex] m
Wavelength of light [tex]\lambda = 558 \times 10^{-9}[/tex] m
According to rayleigh criterion,
[tex]\sin \theta = 1.22 \frac{\lambda}{a}[/tex]
Where [tex]\theta =[/tex] angular resolution, [tex]a =[/tex] diameter of aperture,
For larger diameter [tex]a[/tex],
[tex]\sin \theta _{1} = 1.22 \frac{558 \times 10^{-9} }{8 \times 10^{-3} }[/tex]
[tex]\theta _{1} =[/tex] 0.0049°
For smaller diameter [tex]a'[/tex],
[tex]\sin \theta _{2} = 1.22 \frac{558 \times 10^{-9} }{2 \times 10^{-3} }[/tex]
[tex]\theta _{2} =[/tex] 0.0195°
For finding the angular resolution,
[tex]\theta _{r} = \theta _{2} - \theta _{1}[/tex]
[tex]\theta _{r} = 0.0195 - 0.0049[/tex]
[tex]\theta _{r} =[/tex] 0.0146°
Therefore, the angular resolution is 0.0146°
