Question

Assume that light of wavelength $600\text{nm}$ is coming from a star. The limit of resolution of telescope whose objective has a diameter of $2\text{m}$ is

• A. $7.32\times {10}^{-7}\text{rad}$
• B. $6\times {10}^{-7}\text{rad}$
• C. $3.66\times {10}^{-7}\text{rad}$
• D. $1.83\times {10}^{-7}\text{rad}$

Answer 1

The correct option is C $3.66\times {10}^{-7}\text{rad}$

Given:
Wavelength, $\lambda =600\text{nm}=600\times {10}^{-9}\text{m}$
Diameter, $d=2\text{m}$

Limit of resolution,
$\Delta {\theta }_{min}$$=\frac{1.22\times \lambda }{d}\text{rad}$
$\Rightarrow \Delta {\theta }_{min}$$=\frac{1.22\times 600\times {10}^{-9}}{2}\text{rad}$
$\Rightarrow \Delta {\theta }_{min}$$=3.66\times {10}^{-7}\text{rad}$