A telescope with objective diameter R is used to observe a distant...

The limit of resolution of a telescope is given by the formula:

$\Delta \theta = \dfrac{1.22 \lambda}{R}$

where $\lambda$ is the wavelength of light and $R$ is the diameter of the objective lens.

Given:
$\lambda = 500 \text{ nm} = 500 \times 10^{-9} \text{ m} = 5 \times 10^{-7} \text{ m}$
$\Delta \theta = 5 \times 10^{-7} \text{ rad}$

Substituting the values into the formula:

$5 \times 10^{-7} = \dfrac{1.22 \times 5 \times 10^{-7}}{R}$

$R = 1.22 \text{ m}$

Converting to centimeters:

$R = 1.22 \times 100 \text{ cm} = 122 \text{ cm}$

Answer: $122$