Two points separated by a distance of $0.1\,mm$ can just be resolved in a microscope when a light of wavelength $6000\ \mathring{A}$ is used. If the light of wavelength $4800\ \mathring{A}$ is used,this limit of resolution becomes.......$mm$.

Two poles are separated by a distance of $3.14 \, m$. The resolving power of the human eye is $1 \, min$ of an arc. The maximum distance from which one can identify the two poles distinctly is

$A$ telescope of aperture $3 \times 10^{-2} \, m$ diameter is focused on a window at $80 \, m$ distance fitted with a wire mesh of spacing $2 \times 10^{-3} \, m$. Given: $\lambda = 5.5 \times 10^{-7} \, m$,which of the following is true for observing the mesh through the telescope?

Two luminous point sources separated by a certain distance are at $10 \,km$ from an observer. If the aperture of his eye is $2.5 \times 10^{-3} \,m$ and the wavelength of light used is $500 \,nm$, the distance of separation between the point sources just seen to be resolved is (in $\,m$)

The ratio of resolving powers of an optical microscope for two wavelengths $\lambda_1 = 4000\,\mathring{A}$ and $\lambda_2 = 6000\,\mathring{A}$ is

If the wavelengths of light used in an optical instrument are $\lambda_1 = 4000 \, \mathring A$ and $\lambda_2 = 5000 \, \mathring A$,what will be the ratio of their resolving powers?