Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600 nm, coming from a distant object, the limit of resolution of the telescope is close to:

The correct option is:
$$3\times {10}^{-7}\text{rad}$$

Step-by-Step Explanation:

1. Identify the Formula:
The limit of resolution (angular resolution) of a telescope, denoted by $\theta$, is the minimum angular separation between two point sources that allows them to be resolved as distinct entities. According to Rayleigh's criterion, this limit is given by the formula:
$$\theta =\frac{1.22\lambda }{d}$$
where:
• $\lambda$ is the wavelength of the light coming from the distant object,
• $d$ is the diameter of the objective lens (aperture) of the telescope.

2. Convert the Given Values into Standard SI Units:
• Diameter of the objective lens, $d=250\text{cm}=2.5\text{m}$
• Wavelength of light, $\lambda =600\text{nm}=600\times {10}^{-9}\text{m}=6\times {10}^{-7}\text{m}$

3. Substitute the Values into the Formula:
$$\theta =\frac{1.22\times 6\times {10}^{-7}}{2.5}$$

4. Perform the Calculation:
First, calculate the numerator:
$1.22\times 6=7.32$
Now, divide by the denominator:
$$\theta =\frac{7.32}{2.5}\times {10}^{-7}$$
$$\theta =2.928\times {10}^{-7}\text{rad}$$

5. Round to the Closest Option:
The calculated value $2.928\times {10}^{-7}\text{rad}$ is extremely close to:
$$3\times {10}^{-7}\text{rad}$$