In an optical instrument- microscope, the wavelengths of light used are $\lambda_1 = 6800 \text{ Å}$ and $\lambda_2 = 5100 \text{ Å}$. The ratio of the resolving power of the microscope corresponding to $\lambda_1$ to that for $\lambda_2$ is

$A$ telescope of diameter $2 \ m$ uses light of wavelength $5000 \ \mathring{A}$ for viewing stars. The minimum angular separation between two stars whose image is just resolved by this telescope is

An astronaut is looking down on the Earth's surface from a space shuttle at an altitude of $400 \, km$. Assuming that the astronaut's pupil diameter is $5 \, mm$ and the wavelength of visible light is $500 \, nm$,the astronaut will be able to resolve a linear object of the size of about ........ $m$.

At Kavalur in India,astronomers using a telescope whose objective had a diameter of $1 \, m$ started using a telescope of diameter $2.54 \, m$. This resulted in:

The average distance between the earth and moon is $38.6 \times 10^4 \ km$. The minimum separation between the two points on the surface of the moon that can be resolved by a telescope whose objective lens has a diameter of $5 \ m$ with $\lambda = 6000 \ \mathring{A}$ is ...... $m$.

$A$ person is observing a bacteria through a compound microscope. For better analysis and to improve the resolving power,he should: