Reflection and Refraction

Reflection occurs when a wave bounces off a surface.

The Law of Reflection

$\boxed{\text{angle of incidence} = \text{angle of reflection}}$ $\theta_i = \theta_r$

Key points:

• Angles are always measured from the normal (a line perpendicular to the surface at the point of incidence)
• The incident ray, reflected ray, and normal all lie in the same plane

Types of Reflection

Specular reflection: From smooth surfaces (mirrors, calm water). Parallel rays remain parallel → clear image.

Diffuse reflection: From rough surfaces (paper, walls). Parallel rays scatter in different directions → no clear image, but the surface is visible.

Refraction is the change in direction of a wave when it passes from one medium to another, caused by a change in speed.

Why Does Refraction Occur?

When light enters a denser medium (e.g., air → glass):

• It slows down
• It bends towards the normal

When light enters a less dense medium (e.g., glass → air):

• It speeds up
• It bends away from the normal

Key Rule

• Entering denser medium → bends towards normal → angle of refraction < angle of incidence
• Entering less dense medium → bends away from normal → angle of refraction > angle of incidence
• If light hits the boundary at exactly 90° (along the normal), it passes straight through with no bending

Snell's Law (Higher Tier)

$n_1 \sin \theta_1 = n_2 \sin \theta_2$

Or for light going from air into a material:

$n = \frac{\sin \theta_i}{\sin \theta_r}$

Where $n$ is the refractive index of the material.

When light travels from a denser medium to a less dense medium (e.g., glass → air):

• At small angles, most light refracts out
• As the angle increases, the refracted ray bends more and more away from the normal
• At the critical angle ($\theta_c$), the refracted ray travels along the boundary (90° to the normal)
• Beyond the critical angle, all light is reflected back — this is total internal reflection (TIR)

$\sin \theta_c = \frac{1}{n}$

Applications of TIR

• Optical fibres: Light bounces along the inside of thin glass fibres, used in telecommunications and endoscopes
• Prisms: Used in binoculars and periscopes to reflect light through 90° or 180°
• Diamond sparkle: Diamond has a very high refractive index (n = 2.42), so the critical angle is very small — light undergoes many internal reflections, making it sparkle

Method

1. Place a rectangular glass block on a sheet of white paper
2. Draw around the block
3. Shine a ray of light at the block at a measured angle of incidence
4. Mark the incident ray and the emergent ray with dots
5. Remove the block and draw the refracted ray inside the block
6. Measure the angle of incidence and angle of refraction
7. Repeat for different angles

Expected Results

• Light bends towards the normal when entering the glass
• Light bends away from the normal when leaving the glass
• The emergent ray is parallel to the incident ray but shifted sideways (lateral displacement)

When a wave is refracted:

• Speed changes (this causes the bending)
• Wavelength changes (shorter in denser medium)
• Frequency stays the same (determined by the source)

Since $v = f\lambda$ and $f$ is constant:

• When speed decreases, wavelength decreases
• When speed increases, wavelength increases

• Reflection: angle of incidence = angle of reflection (measured from normal)
• Refraction: waves change direction when entering a different medium due to speed change
• Denser medium → slows down → bends towards normal
• Less dense medium → speeds up → bends away from normal
• Frequency stays constant; speed and wavelength change
• TIR: occurs when angle > critical angle (from dense to less dense)
• Snell's law: $n_1 \sin\theta_1 = n_2 \sin\theta_2$