If an object kept at the least distance of distinct vision is just resolved with light of wavelength $500 \ nm$ and a pupil of diameter $1 \ mm$,at what distance will the object be just resolved if the wavelength is $400 \ nm$ and the pupil diameter is $0.8 \ mm$ (in $cm$)?

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.

$A$ telescope has an objective lens of $10\; m$ diameter and is situated at a distance of $1\; km$ from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is $5000\; \text{\AA}$, is of the order of:

Resolving power of a telescope increases when

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

The wavelengths of light used in an optical instrument are ${\lambda _1 = 4000 \ \text{\AA}}$ and ${\lambda _2 = 5000 \ \text{\AA}}$. The ratio of their respective resolving powers (corresponding to ${\lambda _1}$ and ${\lambda _2}$) is: