What phenomena of light can be explained on the basis of particle theory and wave theory of light?

Two parallel discs are connected by a rigid rod of length $L=0.5 \,m$ centrally. Each disc has a slit oppositely placed as shown in the figure. $A$ beam of neutral atoms is incident on one of the discs axially at different velocities $v$,while the system is rotated at an angular speed of $600 \,rev/s$,so that atoms only with a specific velocity emerge at the other end. Calculate the two largest speeds (in $m/s$) of the atoms that will emerge at the other end.

According to the particle theory of light (Newton's corpuscular theory),what is the velocity of light in a dense medium compared to that in a rare medium?

Two electrons are moving with the same speed $v$. One electron enters a region of a uniform electric field,while the other enters a region of a uniform magnetic field. If the de-Broglie wavelengths of the two electrons after some time are ${\lambda _1}$ and ${\lambda _2}$ respectively,then:

Assertion $(A)$: Photoelectric effect demonstrates the wave nature of light.
Reason $(R)$: The number of photoelectrons is directly proportional to the frequency of light.

Assertion: The specific charge of positive rays is not constant.
Reason: The mass of ions varies with speed.