Explain how Corpuscular theory predicts the speed of light in a medium, say,

No; Wave theory

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.

Hence, we can write the expression:

$c \sin i=v \sin r \ldots$ (i)

Where,

i = Angle of incidence

r = Angle of reflection

c = Velocity of light in air

v = Velocity of light in water

We have the relation for relative refractive index of water with respect to air as:

$\mu=\frac{v}{c}$

Hence, equation (i) reduces to

$\frac{v}{c}=\frac{\sin i}{\sin r}=\mu$     ...(ii)

But, $\mu>1$

Hence, it can be inferred from equation (ii) that v > c. This is not possible since this prediction is opposite to the experimental results of c > v.

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