Looking for classes? Ksquare Career Institute, Bengaluru →
The angular resolution of a 10 cm diameter telescope at a wavelength of 5000 Å is of the order of -
A
$10^{-4}$ rad
B
$10^{-6}$ rad
C
$10^{6}$ rad
D
$10^{-2}$ rad
Detailed Solution
The limit of resolution (smallest angular separation) of a telescope is $\theta \approx \dfrac{1.22\lambda}{D}$, which is of the order of $\dfrac{\lambda}{D}$.
$\lambda = 5000$ Å $= 5 \times 10^{-7}$ m and $D = 10$ cm $= 0.1$ m
$\theta \approx \dfrac{5 \times 10^{-7}}{0.1} = 5 \times 10^{-6}$ rad
With the factor 1.22, $\theta \approx 6.1 \times 10^{-6}$ rad.
So the angular resolution is of the order of $10^{-6}$ rad.
$\lambda = 5000$ Å $= 5 \times 10^{-7}$ m and $D = 10$ cm $= 0.1$ m
$\theta \approx \dfrac{5 \times 10^{-7}}{0.1} = 5 \times 10^{-6}$ rad
With the factor 1.22, $\theta \approx 6.1 \times 10^{-6}$ rad.
So the angular resolution is of the order of $10^{-6}$ rad.