# Is it possible for the index of refraction to be zero in Snell's law?

• Jimmy Chung
In summary, Snell's Law can be applied in refraction when the light ray is along the normal line, but only if the angles are not zero. Utilizing the formula for index of refraction, the index would not be zero as both the speed of light and velocity are positive. If the light ray travels along the normal line, there is no bending and the angles made with the normal are both zero. However, division by zero must be avoided when investigating the applicability of Snell's Law.
Jimmy Chung
Does Snell's law apply in refraction when the light ray is along the normal line? Utilizing snell's law, the index of refraction (n) would be zero.

nr= ni(sin θi)/sinθr

Sin(θi)= 0 therefore, nr=0

However,utilizing the formula for index of refraction (n=c/v), the index of refraction would not be zero as both v and c are positive.

Are light rays along the normal line and not bending refraction at all? If so, which calculation of the index of reflection is correct? Why is the other one wrong?

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If a light ray goes from one medium to a different medium along the normal the speed of light changes according to the ratio of the two media.

Also in this case of normal incidence there is no bending of the light ray and so the angles made by the light ray with the normal are both zero.

In investigating whether Snell's Law applies one has to be careful about any division by zero.

If you wanted to find the refractive index using Snells Law then I can't see why you would want to use zero angles for your experiment. It would be as pointless as wanting to calculate the speed of an object by finding the time for it to move by a zero distance.
0/0 is not determinate.

## 1. What is Snell's Law?

Snell's Law, also known as the law of refraction, is a fundamental principle in optics that describes how light bends when it passes through different mediums with varying refractive indexes. The law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indexes of the two mediums.

## 2. When does Snell's Law apply?

Snell's Law applies whenever light passes through two different mediums with different refractive indexes. This includes situations such as light passing from air to water, or from glass to air.

## 3. How is Snell's Law used in real life?

Snell's Law is used in various everyday applications, such as eyeglasses, camera lenses, and telescopes. It is also used in more complex technologies, such as fiber optics, which rely on the principle of total internal reflection based on Snell's Law.

## 4. What factors can affect the accuracy of Snell's Law?

Snell's Law assumes that the light rays are passing through a homogeneous medium, meaning the refractive index of the medium is constant throughout. In reality, this may not always be the case, especially if the medium has impurities or imperfections. Additionally, the temperature and pressure of the medium can also affect the accuracy of Snell's Law.

## 5. Are there any limitations to Snell's Law?

Snell's Law is a simplified model that does not take into account other factors such as the polarization of light and the wave nature of light. It also does not apply to situations where there is total internal reflection, as the law assumes that light is passing from a more optically dense medium to a less dense medium.

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