Answer:
The speed of light in diamond is less than the speed of light in water
Explanation:
Refraction is the phenomenon that occurs when light (or another type of wave) moves from one medium to another medium, crossing their interface.
When this occurs, the speed of the wave (as well as its direction) changes, according to Snell's law:
[tex]n_1 sin \theta_1 = n_2 sin \theta_2[/tex]
where
n1 and n2 are the refractive index of the two mediums
[tex]\theta_1, \theta_2[/tex] are the angles that the light forms with the normal to the boundary between the two mediums, in the first and the second medium respectively
Moreover, the index of refraction is defined as:
[tex]n=\frac{c}{v}[/tex]
where c is the speed of light in vacuum and v is the speed of light in the medium we are considering.
Substituting this last formula into Snell's law, we get:
[tex]\frac{c}{v_1} sin \theta_1 = \frac{c}{v_2} sin \theta_2\\\frac{sin \theta_1}{v_1}= \frac{sin \theta_2}{v_2}[/tex]
where in this problem, "1" refers to water and "2" refers to diamond.
We can re-write the equation as follows:
[tex]\frac{sin \theta_2}{sin \theta_1}=\frac{v_2}{v_1}[/tex]
The problem tells us that when moving through diamond, the light ray bends toward the normal: this means that the angle in diamond, [tex]\theta_2[/tex], is smaller than the angle in water, [tex]\theta_1[/tex]. So we have
[tex]\frac{sin \theta_2}{sin \theta_1}<1[/tex]
which means
[tex]\frac{v_2}{v_1}<1[/tex]
And therefore,
[tex]v_2 < v_1[/tex]
so the speed of light in diamond is less than the speed of light in water.
