# The width of a telescope apert

The width of a telescope aperture is important because itdetermines what you will be able to resolve.

(a) You are out stargazing with your 13.6-cm telescope. Youpoint your telescope at an interesting formation in the sky, whichyou think is a binary star system. A binary star system consists oftwo stars in orbit around each other. You guess that the averagewavelength coming from the stars is 528 nm. What is the minimumangular separation between the two stars required for yourtelescope to resolve the two stars of the binary system? ___rad

(b) Having graduated with a degree in astronomy, you seek a jobat the Arecibo radio telescope. You use a large radio telescope(300-m diameter) to observe the same binary system that youobserved in part (a). You estimate that the average radio emissionsfrom the system have a wavelength of 4.66 cm. What is the minimumangular separation required for the Arecibo telescope to resolvethe two stars of the binary system? ___ rad

Solution:

Minimum angular separation between two stars required fortelescope to resolve the two stars in binary system is

Theta=(1.22*Lamda)/D ——(i)

Where D= diameter of telescope

Lamda=wavelength of Light.

(a) given , diameter of telescope = 13.6 c.m

Wavelength coming from stars = 528 nm =528×10^-7 c.m.

From equation (i) substitute the values to find out minimumangular separation between two stars is (1.22×528×10^-7)/13.6=4.73×10^-6 radian.

Hence, minimum angular separation between two stars required fortelescope is 4.73×10^-6 radian.

(b) given , diameter of telescope = 300 meter

Wavelength = 4.66 c.m =4.66 ×10^-2 meter

Now substitute the given values in equation(i) to find outminimum angular separation between two stars is (1.22×4.66×10^-2)/300 =1.89×10^-4 radian.

Hence, minimum angular separation between two stars required fortelescope to resolve between two stars is 1.89×10^-4 radian.

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