Question

why is sine used in the formula of refractive index. why not other trigonometric ratios?​

Answer 1

Answer:

Step-by-step explanation:

Choose the angle between the interface and the ray of light, and you have cosines instead of sines. It is just a convention to choose the angle between the normal to the interface and the ray of light, which makes the sine function appear.

More imporant then asking yourself this question, is to understand what it is that Snell’s law describes; that is, the principle of least time. When we model light with rays (we can do it when it’s wavelength is smaller than any object it passes through, so to speak) it happens that the ray always takes the path that will take less time.

While passing through a given medium, like air, the ray will go straight, because that’s the path which will take less time obviously (it is the shortest).

When there is an interface between two mediums, which is when Snell’s law comes into play, the speed of light depends on the refraction index of the two mediums*, so it changes from one to the other. It is slower in the medium with the higher refraction index. Therefore, the ray of light, always wanting to travel the least possible time, will travel a longer distance in the medium with the lower index of refraction, where it travels faster, and a shorter distance in the other medium. The path it takes therefore turns abruptly at the interface, forming two different angles with it.