Question

The Hale telescope of Mount Palomar has a diameter of 200 inch. What is its limiting angle of resolution for 600 nm light?

Answer 1

First of all to solve this problem we have to know what angle of resolution. We can define the angle of resolution as the angle between two points or lines that are far apart. An optical device has the capability to resolve those two points. And it is called the resolving power. So to calculate the limiting angle of resolution use Rayleigh criterion.

Complete step-by-step solution:
Given that,
$d=200$inch
$d=200\times 2.54=508cm=5.08m$
$\lambda =600nm$
$\lambda =600\times {{10}^{-9}}m$
Applying the Rayleigh criterion the equation for limiting angle of resolution is,
$\vartriangle \theta =1.22\left( \dfrac{\lambda }{d} \right)$
Where, $\lambda$wavelength of the light used.
‘d’ is the diameter of the telescope.
Thus substituting the values the equation becomes,
$\begin{aligned} & \vartriangle \theta =1.22\left( \dfrac{\lambda }{d} \right) \\\ & \vartriangle \theta =1.22\left( \dfrac{600\times {{10}^{-9}}}{5.08} \right) \\\ & \vartriangle \theta =1.44\times {{10}^{-7}}radian \\\ \end{aligned}$

Note: While applying the Rayleigh criteria you must know what is the 1.22 used in the above equation. This is a factor used in the case of a circular aperture like the pupil of our eye. These types of apertures are seen in telescopes and cameras. Hence while calculating the limiting angle of resolution we can use this formula. And the resolution means the ability to separate into two images from two source points. The limit of resolution is also known as the resolving power determines the ability of the objective lens to separate images. The Hubble space telescope is the telescope which has the best resolution or the highest resolution. Whereas the resolution indicates the actual detail observed in the image or specimen. While resolving power denotes the smallest detail.