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

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(N/A) No,the prediction is not confirmed. According to Newton's corpuscular theory,when light corpuscles travel from a rarer medium (air) to a denser medium (water),they experience an attractive force normal to the interface. This force increases the normal component of the velocity,while the tangential component remains constant. This leads to the relation $v = \mu c$,where $v$ is the speed in the medium and $c$ is the speed in vacuum. Since the refractive index $\mu > 1$,the theory predicts $v > c$.
This prediction contradicts experimental results,which show that the speed of light in a denser medium is less than in a vacuum $(v < c)$. The wave theory of light,proposed by Huygens,correctly predicts that $v = c / \mu$,which is consistent with experimental observations.

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The figure shows plane waves refracted from air to water using Huygens's principle. $a, b, c, d, e$ are lengths on the diagram. The refractive index of water with respect to air is the ratio:

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What does Huygens' principle explain regarding secondary wavelets?

Describe the short history of light.

$A$ plane wavefront is incident on a water surface at an angle of incidence $60^{\circ}$. It then gets refracted at an angle of $45^{\circ}$. The ratio of the width of the incident wavefront to that of the refracted wavefront is $\left[\sin \frac{\pi}{4}=\cos \frac{\pi}{4}=\frac{1}{\sqrt{2}}, \sin 60^{\circ}=\frac{\sqrt{3}}{2}, \cos 60^{\circ}=\frac{1}{2}\right]$

Huygens' concepts of secondary wavelets:

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