$\lambda_{1}$ and $\lambda_{2}$ are used to illuminate the slits. $\beta_{1}$ and $\beta_{2}$ are the corresponding fringe widths. The wavelength $\lambda_{1}$ can produce photoelectric effect when incident on a metal. But the wavelength $\lambda_{2}$ cannot produce photoelectric effect. The correct relation between $\beta_{1}$ and $\beta_{2}$ is

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 $c = 3 \times 10^{8} \,m/s$)

In the given figure,light of intensity $I$ is incident on a glass slab at point $A$ at an angle of incidence $\theta_1$. It undergoes partial reflection and partial refraction. At each reflection,$25\%$ of the incident energy is reflected. If interference occurs between the rays $AB$ and $A'B'$,then $I_{max}/I_{min} = \dots$ (in $: 1$)

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

The figure shows a schematic diagram of the arrangement of Young's Double Slit Experiment. Choose the correct statement$(s)$ related to the wavelength of light used.

Laser is/are: