A radio telescope 200 m in diameter is used to investigate sources emitting a 21-cm wavelength wave.What is the minimum angular separation of the sources that can be resolved by this system?
A) 0.073°
B) 0.030°
C) 0.0013°
D) 0.154°
E) 0.0026°

Question

Quizplus · Accepted Answer

The minimum angular resolution of a telescope can be calculated using the formula $\theta = \frac{1.22 \lambda}{D}$, where $\theta$ is the angular resolution in radians, $\lambda$ is the wavelength of the light (or other electromagnetic radiation), and $D$ is the diameter of the telescope's aperture. Given $\lambda = 21$ cm = 0.21 m and $D = 200$ m, substituting these values gives $\theta \approx 1.22 \times \frac{0.21}{200} = 0.00127$ radians. Converting to degrees ($1 \text{ radian} = 57.2958^\circ$), $\theta \approx 0.00127 \times 57.2958 = 0.073^\circ$.

A Radio Telescope 200 M in Diameter Is Used to Investigate