Respuesta :
Answer:
Diameter is 486.23 m
Solution:
Wavelength of the light, [tex]\lambda = 50\ nm[/tex]
Distance from the earth, d = [tex]4.30\ ly[/tex]
1 ly = [tex]9.46\times 10^{15}\ m[/tex]
Since, the size of the planet is that of the Jupiter, therefore,
Diameter of the planet, D = [tex]1.38\times 10^{8}\ m[/tex]
Now,
To calculate the minimum diameter:
The angular resolution is given by:
[tex]\theta = \frac{Diameter\ of\ the\ object,\ D}{Distance\ of\ the\ object,\ d}[/tex]
Distance from the earth, d = [tex]4.30\times 9.46\times 10^{15}\ m = 4.067\times 10^{16}\ m[/tex]
Now, putting the appropriate value in the above formula:
[tex]\theta = \frac{1.38\times 10^{8}}{4.067\times 10^{16}} = 3.39\times 10^{- 9}\[/tex]
Also, we know:
[tex]\theta = \frac{1.22\lambda }{D}[/tex]
[tex]\theta = \frac{1.22\times 550\times 10^{- 9}}[1.38\times 10^{- 9}} = 486.23\ m[/tex]
