Question

The angular separation of the two components of a double star is 0.6 microradians, and the light from the double star has a wavelength of 471 nm. What is the diameter (in cm) of the smallest telescope mirror that will resolve the double star?

Answer 1

Diameter, d = 95.7 cm

Step-by-step explanation:

It is given that,

Angular separation of the two components of a double star is,
`\theta=0.6\ \mu\ radian=0.6* 10^(-6)\ rad`

Wavelength of double star,
`\lambda=471\ nm=471* 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=(1.22\lambda)/(d)`

`d=(1.22\lambda)/(\theta)`

`d=(1.22* 471* 10^(-9))/(0.6* 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.