Question

A monochromatic light of wavelength \(6000\ \text{\AA}\) coming from a star is detected in a \(100\)-inch telescope. The limit of resolution of the telescope is approximately

• A. \(3.4\times10^{-7}\ \text{rad}\)
• B. \(6.7\times10^{-7}\ \text{rad}\)
• C. \(2.9\times10^{-7}\ \text{rad}\)
• D. \(1.54\times10^{-7}\ \text{rad}\)

Hint:

For a telescope, \[ \theta=\frac{1.22\lambda}{D}. \] A larger objective diameter \(D\) gives a smaller value of \(\theta\), resulting in better resolving power.

Answer 1

The Correct Option is C

Step 1: Apply Rayleigh criterion for circular aperture.
\( \theta_{min} = \frac{1.22\lambda}{D} \).

Step 2: Substitute values.
\( \lambda = 6000\text{ Å} = 6\times10^{-7}\text{ m} \), \( D = 100\text{ inch} = 100\times0.0254 = 2.54\text{ m} \).
\( \theta_{min} = \frac{1.22\times6\times10^{-7}}{2.54} = \frac{7.32\times10^{-7}}{2.54} \approx 2.9\times10^{-7}\text{ rad} \)

\[ \boxed{\theta_{min} \approx 2.9\times10^{-7}\text{ rad}} \]