Two parallel pillars are $11 \, km$ away from an observer. The minimum distance between the pillars so that they can be seen separately will be.....$m$

$A$ telescope uses light having a wavelength of $5000 \, \mathring{A}$ and lenses with focal lengths of $2.5 \, \text{cm}$ and $30 \, \text{cm}$. If the diameter of the aperture of the objective is $10 \, \text{cm}$,what are the resolving limit and the magnifying power of the telescope,respectively?

The resolving power of an astronomical telescope is $0.2$ seconds. If the central half portion of the objective lens is covered,the resolving power will be......$sec$

Assertion : $A$ famous painting was painted by not using brush strokes in the usual manner,but rather a myriad of small colour dots. In this painting the colour you see at any given place on the painting changes as you move away.
Reason : The angular separation of adjacent dots changes with the distance from the painting.

$A$ microscope was initially placed in air (refractive index $1$). It is then immersed in oil (refractive index $2$). For a light whose wavelength in air is $\lambda$,calculate the change of the microscope's resolving power due to oil and choose the correct option.

The resolving power of a compound microscope will be maximum when