Explain how Corpuscular theory predicts the speed of light in a medium, say, water, to be greater than the speed of light in vacuum. Is the prediction confirmed by experimental determination of the speed of light in water? If not, which alternative picture of light is consistent with experiment?

Explanation

According to Newton.s corpuscular theory, when a light ray enters obliquely from rarer to denser medium, constituent particles of incident light ray experience force of attraction, normal (perpendicular) to the interface, which increases their normal velocity but the tangential (parallel) velocity remains unaffected.

s shown in the diagram, consider a ray of light PQ, moving with velocity c in air, made incident on the surface AB of denser transparent medium of water having refractive index `mu_(wa)` with respect to air.
Inside the water, refracted ray QR moves with velocity v. Here `anglePQM`= angle of incidence = i, `angleRQN`= angle of refraction =r.
As shown in the diagram, tangential velocity of incident ray is c sini whereas tangential velocity of refracted ray is v sinr.
Now, according to Newton.s corpuscular theory (particle theory), tangential velocity remains constant. Hence,
`csini=vsinr`
`:.(sini)/(sinr)=(v)/(c)`
`:.mu_(wa)=(v)/(c)" "(""mu_(wa)=(sini)/(sinr))`
But `mu_(wa)=(mu_(w))/(mu_(a))gt1" "("":.mu_(w)gtmu_(a))`
`implies(v)/(c)gt1`
`impliesvgtc`
Thus, Newton.s theory predicts that light ray travels faster in water as compared to air.
But experimentally we find that `vltc`, which proves that Newton.s prediction was wrong. Later, Huygens had proposed wave theory of light which is quite consistent and true with the experimental observation.