Question

Assume that light of wavelength $600\, nm$ is coming from a star. The limit of resolution of telescope whose objective has a diameter of $2\,m$ is :

• A. $3.66 \times 10^{-7} \,rad$
• B. $1.83 \times 10^{-7} \,rad$
• C. $7.32 \times 10^{-7} \,rad$
• D. $6.00 \times 10^{-7} \,rad$

Answer 1

The Correct Option is A

To determine the limit of resolution of a telescope, we use the formula for the angular resolution (or resolving power) of a circular aperture, such as the objective lens of a telescope:

\(\theta_{\text{min}} = 1.22 \frac{\lambda}{D}\)

where:

• \(\theta_{\text{min}}\) is the minimum resolvable angle in radians.
• \(\lambda\) is the wavelength of light, which is \(600 \, \text{nm} = 600 \times 10^{-9} \, \text{m}\).
• \(D\) is the diameter of the telescope's objective, which is \(2 \, \text{m}\).

Substitute the given values into the formula:

\(\theta_{\text{min}} = 1.22 \frac{600 \times 10^{-9} \, \text{m}}{2 \, \text{m}}\)

Calculate:

\(\theta_{\text{min}} = 1.22 \times 300 \times 10^{-9} \, \text{rad}\)

\(\theta_{\text{min}} = 3.66 \times 10^{-7} \, \text{rad}\)

Thus, the limit of resolution of the telescope is \(3.66 \times 10^{-7} \, \text{rad}\).

Therefore, the correct answer is:

\(3.66 \times 10^{-7} \, \text{rad}\)

This option matches with:

\(3.66 \times 10^{-7} \, \text{rad}\)