Answer
a). (3) blue
b). $\theta_{min}=0.004^{\circ}$ for 400-nm light
and $\theta_{min}=0.007^{\circ}$ for 700-nm light.
Work Step by Step
a). (3) For blue color the human eye can see the finest details because as per the minimum angle of resolution equation :
$\theta_{min}=\frac{1.22\times wavelength}{D}$
D is fixed as pupil of human eye has nearly same diameter.
Hence more is the wavelength more will be the value of $\theta_{min}$ and less fine will be the details that can be observed by human eye.
b). $\theta_{min}=\frac{1.22\times wavelength}{D}$
for wavelength, $lambda_{1}$:
$\theta_{min}=\frac{1.22\times wavelength}{D}=\frac{1.22\times400\times10^{-9}}{7\times 10^{-3}}=0.004^{\circ}$
for wavelength, $lambda_{2}$:
$\theta_{min}=\frac{1.22\times wavelength}{D}=\frac{1.22\times700\times10^{-9}}{7\times 10^{-3}}=0.007^{\circ}$
