Reflection, Refraction, and Diffraction

• Law of reflection: angle of incidence = angle of reflection ($\theta_i = \theta_r$)
• Angles measured from the normal
• Applies to all waves (light, sound, water)

When a wave passes from one medium to another, its speed changes, causing the wave to bend.

Snell's Law

$\boxed{n_1 \sin\theta_1 = n_2 \sin\theta_2}$

$n = c/v$ (refractive index)

• Into denser medium: speed decreases, bends towards normal
• Into less dense medium: speed increases, bends away from normal
• Frequency remains constant; wavelength changes

Conditions:

1. Light travels from denser to less dense medium
2. Angle of incidence > critical angle $\theta_c$

$\sin\theta_c = \frac{n_2}{n_1}$

Applications: optical fibres, prisms, bicycle reflectors.

Waves spread out when passing through a gap or around an obstacle.

• Maximum diffraction when gap width ≈ wavelength
• Wider gap → less diffraction
• Longer wavelength → more diffraction

Diffraction explains why we can hear around corners (sound wavelength ~ door width) but light doesn't bend around corners noticeably (very short wavelength).

• Reflection: $\theta_i = \theta_r$
• Refraction: $n_1\sin\theta_1 = n_2\sin\theta_2$; frequency constant, speed and $\lambda$ change
• TIR: denser → less dense, $\theta > \theta_c$; $\sin\theta_c = n_2/n_1$
• Diffraction: significant when gap ≈ wavelength