Answer:
The value is [tex]\theta _2 = 0.08 \ arcsec[/tex]
Explanation:
From the question we are told that
The first wavelength is [tex]\lambda_1 = 660 \ nm = 660 *10^{-9 }[/tex]
The first angular size is [tex]\theta_1 = 0.04 \ arcsec[/tex]
The second wavelength is [tex]\lambda _2 = 1320 \ nm = 1320 *10^{-9 } \ m[/tex]
Generally according to Rayleigh Criterion we have that
[tex]\theta= 1.22 * \frac{\lambda }{D}[/tex]
given every other thing remains constant we have that
[tex]\theta = k * \lambda[/tex]
Here k represented constant so
[tex]k = \frac{\theta }{\lambda}[/tex]
=> [tex]\frac{\theta_1}{ \lambda_1} = \frac{\theta_2}{ \lambda_2}[/tex]
=> [tex]\frac{\theta_1}{ \theta_2} = \frac{\lambda_1}{ \lambda_2}[/tex]
So
[tex]\frac{ 0.04}{ \theta_2} =0.5[/tex]
=> [tex]\theta _2 = 0.08 \ arcsec[/tex]
