If an optical telescope focusing light of wavelength 550 nm had a perfectly ground mirror, what would have to be the minimum diameter of its mirror so that it could resolve a jupiter-size planet around our nearest star, alpha centauri, which is about 4.30 light years from earth? (1 light year = 9.46×1015 m )

Diameter is 486.23 m

Solution:

Wavelength of the light,

Distance from the earth, d =

1 ly =

Since, the size of the planet is that of the Jupiter, therefore,

Diameter of the planet, D =

Now,

To calculate the minimum diameter:

The angular resolution is given by:

Distance from the earth, d =

Now, putting the appropriate value in the above formula:

Also, we know:

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