Which of the following phenomena support the wave theory of light?
$(1)$ Scattering
$(2)$ Interference
$(3)$ Diffraction
$(4)$ Velocity of light in a denser medium is less than the velocity of light in a rarer medium

The maximum illumination on a screen at a distance of $2\, m$ from a lamp is $25\, lux.$ The value of total luminous flux emitted by the lamp is

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:

$A$ screen receives $3 \ W$ of radiant flux of wavelength $6000 \ \mathring{A}.$ One lumen is equivalent to $1.5 \times 10^{-3} \ W$ of monochromatic light of wavelength $5550 \ \mathring{A}.$ If the relative luminosity for $6000 \ \mathring{A}$ is $0.685$ while that for $5550 \ \mathring{A}$ is $1.00,$ then the luminous flux of the source is:

$A$ circular disc of which $2/3$ part is coated with yellow and $1/3$ part is with blue. It is rotated about its central axis with high velocity,then it will be seen as

$\lambda_{1}$ 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