Understanding Light Refraction: Rarer to Denser Medium

When a ray of light travels from one transparent medium to another, it changes direction. This phenomenon is called refraction. The extent to which a medium can refract light is related to its optical density. We often compare media as 'rarer' or 'denser' based on this property.

• A rarer medium (optically rarer) is one where the speed of light is higher. Examples include air or vacuum.
• A denser medium (optically denser) is one where the speed of light is lower. Examples include water or glass.

Effect on Speed When Light Enters a Denser Medium

The speed of light is not constant in all media. It depends on the properties of the medium. When light moves from an optically rarer medium to an optically denser medium, its speed decreases. This is because the denser medium interacts more with the light waves, slowing them down.

Mathematically, the refractive index (\(n\)) of a medium is defined as the ratio of the speed of light in vacuum (\(c\)) to the speed of light in that medium (\(v\)):

\(n = \frac{c}{v}\)

A denser medium has a higher refractive index, which implies a lower speed of light (\(v = c/n\)). So, moving from a rarer medium (lower \(n\), higher \(v\)) to a denser medium (higher \(n\), lower \(v\)) results in the light slowing down.

Effect on Bending When Light Enters a Denser Medium

Besides changing speed, the light ray also changes direction when it enters a different medium at an angle (not perpendicularly). This bending is relative to an imaginary line called the 'normal'. The normal is a line drawn perpendicular to the surface separating the two media at the point where the light ray hits the surface.

• When light travels from an optically rarer medium to an optically denser medium, the ray bends towards the normal.
• When light travels from an optically denser medium to an optically rarer medium, the ray bends away from the normal.

This bending occurs because different parts of the wavefront of light enter the new medium at different times, causing the wavefront to pivot.

Summary for Rarer to Denser Medium

Based on the principles of refraction:

When a ray of light travels from a rarer medium to a denser medium:

• Its speed slows down.
• It bends towards the normal.

Let's look at the options provided:

• Option 1: slows down and bends away from the normal. (Incorrect - bends towards)
• Option 2: slows down and bends towards the normal. (Correct)
• Option 3: speeds up and bends away from the normal. (Incorrect - slows down and bends towards)
• Option 4: speeds up and bends towards the normal. (Incorrect - slows down)

Therefore, the correct statement is that the light ray slows down and bends towards the normal when travelling from a rarer medium to a denser medium.

Revision Table: Light Refraction

Additional Information: Refractive Index and Snell's Law

The refractive index (\(n\)) is a fundamental property of a medium that determines how much light slows down and bends in it. A higher refractive index means higher optical density.

The relationship between the angles of incidence and refraction and the refractive indices of the two media is described by Snell's Law:

\(n_1 \sin(\theta_i) = n_2 \sin(\theta_r)\)

Where:

• \(n_1\) is the refractive index of the first medium (where light comes from).
• \(n_2\) is the refractive index of the second medium (where light enters).
• \(\theta_i\) is the angle of incidence (angle between the incoming ray and the normal).
• \(\theta_r\) is the angle of refraction (angle between the refracted ray and the normal).

If light goes from rarer to denser, \(n_1 < n_2\). According to Snell's Law, this requires \(\sin(\theta_i) > \sin(\theta_r)\) for positive angles, which means \(\theta_i > \theta_r\). An angle of refraction smaller than the angle of incidence signifies that the ray has bent towards the normal.