$A$ source of light emits a continuous stream of light energy which falls on a given area. Luminous intensity is defined as

Statement $(S)$: Using Huygen's eye-piece,measurements can be taken but are not correct.
Reason $(R)$: The cross wires,scale,and final image are not magnified proportionately because the image of the object is magnified by two lenses,whereas the cross-wire scale is magnified by one lens only.
Identify the correct option from the following:

The intensity of light from a continuously emitting laser source operating at $638 \,nm$ wavelength is modulated at $1 \,GHz$. The modulation is done by momentarily cutting the intensity off with a frequency of $1 \,GHz$. What is the farthest distance apart two detectors can be placed in the line of the laser light,so that they can see the portions of the same pulse simultaneously?
(Consider the speed of light in air $c = 3 \times 10^{8} \,m/s$)

Light of different colours propagates through air:

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is $1$. The thickness of the air column is $....\,mm$. [Refractive index of air $= 1.0003$,wavelength of yellow light in vacuum $= 6000\,\mathring{A}$]

$A$ carrot looks orange in colour because of the $\beta$-carotene molecule in it. This means that the $\beta$-carotene molecule absorbs light of wavelengths