The relationship between the amount of bending and the index of refraction when light passes from an optically less dense medium to a denser one is directly proportional.

Here's a breakdown:

* Index of Refraction (n): This is a measure of how much light slows down when it enters a medium. A higher index of refraction means the light slows down more.

* Bending (Refraction): When light passes from one medium to another with a different index of refraction, it changes direction. This bending is called refraction.

The key relationship:

* Higher index of refraction: The greater the difference in the indices of refraction between the two media, the more the light will bend.

* Example: Light passing from air (n ≈ 1.00) to water (n ≈ 1.33) will bend more than light passing from air to glass (n ≈ 1.5).

Why this happens:

* Snell's Law: This law describes the relationship between the angle of incidence (the angle at which light strikes the boundary), the angle of refraction, and the indices of refraction of the two media. It essentially states that light bends towards the normal (an imaginary line perpendicular to the surface) when it enters a medium with a higher index of refraction.

In summary: The more the light slows down (higher index of refraction), the more it will bend as it enters the denser medium.