Because light travels more quickly in D. glass than in diamond
Explanation:
Refraction is a phenomenon of light waves that occurs when a light way crosses the boundary between two different mediums. When this happens, the wave changes its direction and also its speed. In particular, there is an equation (called Snell's law) that descrives the direction of the refracted ray relative to the incident ray:
[tex]n_1 sin \theta_1 = n_2 sin \theta_2[/tex]
where
[tex]n_1, n_2[/tex] are the index of refraction of medium 1 and 2, respectively
[tex]\theta_1[/tex] is the angle of incidence (the angle between the incident ray and the normal to the boundary between the two mediums)
[tex]\theta_2[/tex] is the angle of refraction (the angle between the refraction ray and the normal to the boundary between the two mediums)
The equation can also be written as
[tex]\frac{sin \theta_2}{sin \theta_1}=\frac{n_1}{n_2}[/tex] (1)
The index of refraction of a medium is equal to
[tex]n=\frac{c}{v}[/tex]
where
c is the speed of light in a vacuum
v is the speed of light in the medium
Using this, we can rewrite (1) as
[tex]sin \theta_2 = \frac{n_1}{n_2}sin \theta_1 = \frac{v_2}{v_1} sin \theta_1[/tex]
where [tex]v_2[/tex] is the speed of light in the 2nd medium and [tex]v_1[/tex] the speed of light in the 1st medium.
Here we are comparing two situations:
1) Light passing from air to glass
2) Light passing from air to diamond
We are said that light is refracted by a greater amount when it passes from air to diamond: this means that in situation 2), the value of [tex]sin \theta_2[/tex] is smaller than in situation 1) (keep in mind that the angle is measured with respect to the normal, so a larger refraction means a smaller angle, since the refracted ray bends towards the normal). And therefore, this means that the ratio [tex]\frac{v_2}{v_1}[/tex] is smaller for case 2) rather than for case 1): since [tex]v_1[/tex] in both cases is the same (the speed of light in air), this means that light travels more quickly in glass than in diamond, so option D.
In fact, by comparison:
Index of refraction in glass: 1.66
Index of refraction in diamond: 2.41
Which means that light travels faster in glass.
Learn more about refraction:
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