Physics, 27.12.2019 10:31 rniadsharri16

Aray of light is traveling from water into a diamond. upon hitting the diamond, a light ray bends toward the normal. with this information, what can you say about the speed of light as it passes from water into a diamond?

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As the light pass through different media, it experiences a refraction. This is a phenomenon where the speed and direction of light changes. If the ray of light moves towards the normal line, the angle is decreased. So, is the speed of that light.

Answer from: BlackMilkTea

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:

$n_1 sin \theta_1 = n_2 sin \theta_2$

where

n1 and n2 are the refractive index of the two mediums

$\theta_1, \theta_2$ 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:

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

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:

$\frac{c}{v_1} sin \theta_1 = \frac{c}{v_2} sin \theta_2\\\frac{sin \theta_1}{v_1}= \frac{sin \theta_2}{v_2}$

where in this problem, "1" refers to water and "2" refers to diamond.

We can re-write the equation as follows:

$\frac{sin \theta_2}{sin \theta_1}=\frac{v_2}{v_1}$

The problem tells us that when moving through diamond, the light ray bends toward the normal: this means that the angle in diamond, $\theta_2$ , is smaller than the angle in water, $\theta_1$ . So we have

$\frac{sin \theta_2}{sin \theta_1}$

which means

$\frac{v_2}{v_1}$

And therefore,

v_2 < v_1

so the speed of light in diamond is less than the speed of light in water.

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