Question

How can the resolving power of a telescope be increased?

Answer 1

The resolving power of a telescope is the reciprocal of the smallest angular separation between two distant objects whose image is just seen separately. It is also the reciprocal of the limit of resolution of the telescope.

Formula used:
$RP= \dfrac{1}{limit\;of\;resolution}=\dfrac{a}{1.22\lambda}$

Complete step by step answer:
When the light of comparable wavelength falls on a circular opening like a lens, this results in a blurred image called the airy disc. This occurs due to the overlapping of the wavelengths at the circular opening. The half-angle of the first minimum is given by:$\sin\theta\approx 1.22\dfrac{\lambda}{a}$
In order to obtain point images, the source must be just resolved. The criterion for the image to be just resolved is given by Rayleigh and is called the Rayleigh Criterion. It states: two point sources are said to be just resolved if the principal diffraction maximum of the first image coincides with the first minimum of the other.
The resolving power of a telescope is the reciprocal of the smallest angular separation between two distant objects whose image is just seen separately. It is also the reciprocal of the limit of resolution of the telescope.
It given as $RP= \dfrac{1}{limit\;of\;resolution}=\dfrac{a}{1.22\lambda}$ where $a$ is the diameter of the objective lens of the telescope and $\lambda$ is the wavelength of the incident light.
Thus clearly, $RP\propto a$ and $RP\propto \dfrac{1}{\lambda}$. As the wavelength of the incident light is fixed, we can increase the resolving power by increasing the diameter of the objective lens.
Hence, in order to increase the resolving power, the diameter of the objective lens can be increased.

Note:
Limit of resolution $\theta=1.22\dfrac{\lambda}{a}$, whereas resolving power $RP= \dfrac{1}{limit\;of\;resolution}=\dfrac{a}{1.22\lambda}$. Students tend to confuse between the two. It is suggested that you remember one, and take the reciprocal to find the other. Also, $RP\propto a$ and $RP\propto \dfrac{1}{\lambda}$. As the wavelength of the incident light is fixed, we can increase the resolving power by increasing the diameter of the objective lens.