The resolution of a microscope describes the scale of the smallest detail that is clearly observable through the microscope. for a microscope with a moderately high-quality objective lens, the resolution is approximately equal to the wavelength of light used. by this criteria, what is the smallest detail observable with a microscope that uses ultraviolet light of frequency 1.19\times 10^{15}~\text{hz}1.19×10 15 hz?

Resolution = Wavelength = 252.101 nm

Explanation:

The relation between frequency and wavelength is shown below as:

c is the speed of light having value

Given, Frequency =

Thus, Wavelength is:

Also, 1 m = nm

So,

Resolution = Wavelength = 252.101 nm

firearm identification is the process of analyzing the bullets and cartridge cases left at a crime scene to determine if they came from a particular firearm. marks on the bullets and cartridges may be common to every firearm of that type. these are called class characteristics.

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.