Question

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?

Answer 1

In Newton's corpuscular (particle) picture of refraction, particles of light incident from rarer to denser medium experience a force of attraction normal to he surface. this results in an increase in the normal component of velocity but the component of velocity along the the surface remains unchanged.

Let's consider a ray of light going from a rarer medium( like air or vaccum to a denser medium( like water ).

let c denotes the speed of light in vaccum /air

and v is the speed of light in water.

i is angle of incidence and r is the angle of refraction.

then, according to Newton's corpuscular theory,

component of velocity c along the surface of seperation = component of v along the surface of seperation.

see figure,

component of velocity c along the surface of seperation = csini

component of velocity v along the surface of seperation = vsinr

so, csini = vsinr

or, v/c = sini/sinr = $\frac{\mu_g}{\mu_a}$

as  $\frac{\mu_g}{\mu_a}$  > 1

so, v/c > 1

or, v > c

so, according to Newton's corpuscular theory, the speed of light in medium is larger than speed of light in vaccum/air. but in fact the experimental observation shows that speed of light is smaller in denser medium as compared to rare medium. v < c.

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Answer 2

Explanation:

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$\sf \longrightarrow\:No;\:wave\:theory$

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$\hookrightarrow$ Newton's Corpuscular theory states that light when light corpuscules strike the interface of two media from a rarer(air) to 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

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Hence, we can write the expression

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$\sf v\sin\,i\:=\:v\sin\,r \longrightarrow\:(i)$

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$\textsf{i = angle of incidence}$

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$\textsf{r = angle of reflection}$

$\textsf{c = Velocity of light in air}$

$\textsf{v = Velocity of light in water}$

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

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$\sf \mu\:=\: \dfrac{v}{c}$

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Hence, equation(i) reduces to

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$\sf \dfrac{v}{c}\:=\: \dfrac{\sin\,i}{\sin\,r}\:=\: \mu$

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but $\sf \mu\:>\:1$

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

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Therefore, the wave picture of light is consistent with the experimental results