The aperture of the objective is $$24.4$$ cm. The resolving power of this telescope, if a light of wavelength $$2440$$ Å is used to see the object will be

We need to find the resolving power of a telescope with aperture $$D = 24.4$$ cm and wavelength $$\lambda = 2440$$ Å. Converting units gives $$D = 24.4$$ cm $$= 0.244$$ m and $$\lambda = 2440$$ Å $$= 2440 \times 10^{-10}$$ m $$= 2.44 \times 10^{-7}$$ m.

The angular limit of resolution (Rayleigh criterion) is $$\theta = \frac{1.22\lambda}{D}$$, and the resolving power is $$\frac{1}{\theta} = \frac{D}{1.22\lambda}$$. Substituting into this expression gives

$$\frac{0.244}{1.22 \times 2.44 \times 10^{-7}}$$

$$=\frac{0.244}{2.9768 \times 10^{-7}}$$

$$=\frac{2.44 \times 10^{-1}}{2.9768 \times 10^{-7}}$$

$$=8.196 \times 10^5$$

$$\approx 8.2 \times 10^5$$

The correct answer is Option C.