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It is not, so the question is based on a fundamental misunderstanding.

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Q: Why is the index of refraction always greater than 1?
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Why the index of refraction is greater than to one?

It is because the index is related to the velocity of light in air (ideally vacuum) and the medium in question. Since the velocity of light in vacuum is greater than it can be in any other media, the index of refraction of these other media relative to the vacuum is greater than 1.However, if you studied light travelling through glass and then water, the index of refraction between those two would be 0.89 (approx).


What is the ratio of the speed of light in a vacuum to the speed of light in a different medium?

This is called the index of refraction. When light crosses the boundary between mediums (media) with different indices, it is bent (refracted).It's usually defined the other way around ... the ratio of the speed of light in vacuum to its speed in the medium. Since the speed of light is greater in vacuum than in any medium, the number is always greater than 1. It's referred to as the "refractive index" of the medium.


Why is the angle of incidence greater than the angle of refraction based on the magic pencil activity?

The angle of incidence is greater.


What is the index of refraction of sugar?

Crystaline sugar (sucrose) has a refractive index of around 1.56. Sugar solutions can have refractive indices greater than this. Note, that the refractive index of a substance can even be determined for opaque substances. This is because the RI also determines reflective properties. So by measuring the amount of light reflected by light shining on a polished sample at a given angle, a refractive index can in principle be obtained.


Is a prime number always greater than 1?

Yes, a prime number is always greater than 1.