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12345 [234]
3 years ago
10

The angular separation of the two components of a double star is 0.6 microradians, and the light from the double star has a wave

length of 471 nm. What is the diameter (in cm) of the smallest telescope mirror that will resolve the double star?
Physics
1 answer:
Sav [38]3 years ago
3 0

Answer:

Diameter, d = 95.7 cm

Explanation:

It is given that,

Angular separation of the two components of a double star is, \theta=0.6\ \mu\ radian=0.6\times 10^{-6}\ rad

Wavelength of double star, \lambda=471\ nm=471\times 10^{-9}\ m

Let d is the diameter of the smallest telescope mirror that will resolve the double star. The formula for the angular separation is given by :

\theta=\dfrac{1.22\lambda}{d}

d=\dfrac{1.22\lambda}{\theta}

d=\dfrac{1.22\times 471\times 10^{-9}}{0.6\times 10^{-6}}

d=0.957\ m

or

d = 95.7 cm

So, the diameter of the smallest telescope mirror that will resolve the double star is 95.7 cm. Hence, this is the required solution.

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