Question

The Hubble Space Telescope in orbit above the Earth has a 2.4 m circular aperture. The telescope has equipment for detecting ultraviolet light. What is the minimum angular separation between two objects that the Hubble Space Telescope can resolve in ultraviolet light of wavelength 95 nm.
a.7.0 ×10–8 radb.3.3 ×10–9 radc.1.9 ×10–7 radd.4.8 × 10–8 rad

Answer 1

Answer:

Option d

The minimum angular separation between two objects that the Hubble Space Telescope can resolve is $4.8x10^{-8}rad$.  

Explanation:

The resulting image in a telescope that will be gotten from an object is a diffraction pattern instead of a perfect point (point spread function (PSF)).

That diffraction pattern is gotten because the light encounters different obstacles on its path inside the telescope (interacts with the walls and edges of the instrument).

 

The diffraction pattern is composed by a central disk, called Airy disk, and diffraction rings.    

 

The angular resolution is defined as the minimal separation at which two sources can be resolved one for another, or in other words, when the distance between the two diffraction pattern maxima is greater than the radius of the Airy disk.

The angular resolution can be determined in analytical way by means of the Rayleigh criterion.          

$\theta = 1.22\frac{\lambda}{D}$  (1)

Where $\lambda$ is the wavelength and D is the diameter of the telescope.

Notice that it is necessary to express the wavelength in the same units than the diameter.

$\lambda = 95nm \cdot \frac{1x10^{-9}m}{1nm}$ ⇒ $9.5x10^{-8}m$

Finally, equation 1 can be used.

$\theta = 1.22(\frac{9.5x10^{-8}m}{2.4m})$

$\theta = 4.8x10^{-8}rad$              

Hence, the minimum angular separation between two objects that the Hubble Space Telescope can resolve is $4.8x10^{-8}rad$.