10.12 Explain how Corpuscular theory predicts the speed of light in a medium, say, water, to be greater than the speed of light in a 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 the experiment?

Hint: Recall Newton's corpuscular theory of light.

Step 1: Varify Newton's corpuscular theory of light.
This prediction is not confirmed by experimental determination of the speed of light in water. Wave theory is consistent with the given experiment.

Newton's corpuscular theory of light states that when light corpuscles strike the Interface of two media from a rarer (air) to a denser (water) medium, the particles experience forces of attraction normal to the surface. Hence, the normal component of velocity increases while the component along the surface remains unchanged.
Step 2: Draw a diagram.


Hence, we can write the expression as:
c sin i = v sin r …(i)
Where,
i = Angle of Incidence
r = Angle of rejection
c = velocity of light in air
v = Velocity of light in water
The relative refractive index of water with respect to air is given by the relation :
\(\nu=\frac{v}{c } \)


Hence, equation (i) will be:

vc=sinisinr=μ(ii)

But μ > 1

Hence, from equation (ii) we can say that v > c which is not possible since this
prediction is opposite to the experimental results of c > v.

The wave theory of light is consistent with the experimental results.