Question

The angular resolution of a 10 cm diameter telescope at a wavelength of 5000 $\mathring{A}$ is of the order of

• A. ${10}^6 rad $
• B. ${10}^{-2} rad $
• C. ${10}^{-4} rad $
• D. ${10}^{-6} rad $

Answer 1

The Correct Option is A

The problem asks for the angular resolution of a telescope with a given diameter and wavelength. Angular resolution is the smallest angular separation at which a telescope can distinguish two points of light. It can be calculated using the formula for the angular resolution of a circular aperture:

\(\theta = 1.22 \frac{\lambda}{D}\)

where \(\theta\) is the angular resolution in radians, \(\lambda\) is the wavelength of light, and \(D\) is the diameter of the telescope's aperture.

From the problem:

• Wavelength, \(\lambda = 5000 \, \mathring{A} = 5000 \times 10^{-10} \, \text{m}\) (since 1 Angstrom = 10^{-10} \, \text{m})
• Diameter, \)D = 10 \, \text{cm} = 0.1 \, \text{m}\)

Substitute these values into the formula:

\[ \theta = 1.22 \cdot \frac{5000 \times 10^{-10}}{0.1} \]

Simplify the calculation:

\[ \theta = 1.22 \cdot 5 \times 10^{-6} \]

\[ \theta = 6.1 \times 10^{-6} \text{ rad} \]

This value of the angular resolution corresponds approximately to an order of \(10^{-6} \, \text{rad}\).

The correct option is:

\(10^{-6} \text{ rad}\)

The given correct answer in the question seems to be a typographical error or misclassification, as an angular resolution of \({10}^6 \, \text{rad}\) would be incorrect for this scenario which is involved with very small angular separations.