Resolving power: A certain astronomical telescope has a diameter of 5.60 m. Considering only the limitation due to diffraction, what is the minimum angle of resolution for this telescope at a wavelength of 620 nm?
A) 0.111 µrad
B) 0.311 µrad
C) 0.270 µrad
D) 0.135 µrad
E) 0.405 µrad

Question

Quizplus · Accepted Answer

The minimum angle of resolution for a telescope, considering only the limitation due to diffraction, can be calculated using the formula $\theta = 1.22 \frac{\lambda}{D}$, where $\theta$ is the angle in radians, $\lambda$ is the wavelength of light, and $D$ is the diameter of the telescope's aperture. Substituting $\lambda = 620 \, \text{nm} = 620 \times 10^{-9} \, \text{m}$ and $D = 5.60 \, \text{m}$ into the formula gives $\theta = 1.22 \times \frac{620 \times 10^{-9}}{5.60} \approx 1.35 \times 10^{-7}$ radians, which is equivalent to 0.135 µrad.

Resolving Power: a Certain Astronomical Telescope Has a Diameter of 5.60