Which expression correctly represents the refractive index (n) concerning the angles of incidence (i) and refraction (r)?

sin(i) ÷ sin(r)

The refractive index (n) is defined by Snell's Law, which relates the angles of incidence and refraction to the indices of refraction of the two media involved. According to this relationship, the refractive index can be calculated using the formula n = sin(i) / sin(r), where 'i' is the angle of incidence and 'r' is the angle of refraction.

The reasoning for this relationship stems from the behavior of light as it travels from one medium into another, such as air into water. The sine of the angles represents the ratio of the velocities of light in those two media. Therefore, when you take the sine of the angle of incidence and divide it by the sine of the angle of refraction, you effectively obtain the refractive index that quantifies how much the speed of light is reduced in the second medium compared to the first.

In summary, the correct expression for the refractive index is derived from the principles of wave physics and describes how light behaves when transitioning between different materials, confirming that sin(i) / sin(r) accurately represents this relationship.

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sin(r) ÷ sin(i)

i ÷ r

r ÷ i

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