When a wave moves from a less dense to a more dense medium (e.g., air to water), it bends toward the normal.
Conversely, when it moves from a more dense to a less dense medium, it bends away from the normal.
Critical Angle And Total Internal Reflection
When light travels from a medium with a higher refractive index to a lower refractive index (for example, glass to air), it refracts away from the normal.
As the angle of incidence increases, the refracted angle increases even more, until a special limiting case is reached.
Definition
Critical angle $\theta_c$
The angle of incidence in the higher-index medium for which the angle of refraction is 90° (the refracted ray travels along the boundary).
Snell's law is: $$n_1 \sin \theta_1=n_2 \sin \theta_2$$
At the critical angle, $\theta_2=90^{\circ}$, so: $$n_1 \sin \theta_c=n_2 \sin 90^{\circ}=n_2$$ $$\sin \theta_c=\frac{n_2}{n_1}$$
Note
Important condition: A critical angle only exists if $n_1>n_2$.
If $n_1 \leq n_2$, then $\frac{n_2}{n_1} \geq 1$, so there is no single limiting angle that makes $\theta_2=90^{\circ}$.
Definition
Total internal reflection (TIR)
If the angle of incidence is greater than the critical angle $\left(\theta_1>\theta_c\right)$, refraction cannot occur. Instead, all of the light reflects back into the original medium.
For $\theta_1>\theta_c$, Snell's law would require: $$\sin \theta_2=\frac{n_1}{n_2} \sin \theta_1$$
But when $n_1>n_2$ and $\theta_1$ is large enough, this expression becomes greater than 1, and $\sin \theta_2>1$ is impossible.
That means there is no refracted ray, so the wave is reflected entirely back into medium 1.
Diffraction: Bending Around Obstacles
Definition
Diffraction
Diffraction is the spreading of waves as they pass through an aperture or around an obstacle.
This phenomenon is most pronounced when the size of the aperture or obstacle is comparable to the wavelength of the wave.
How Diffraction Works
Consider water waves approaching a narrow gap in a barrier.
As the waves pass through the gap, they spread out in circular patterns.
The smaller the gap relative to the wavelength, the more pronounced the diffraction.
Example
Diffraction explains why you can hear sound around a corner but cannot see around it.
Sound waves have longer wavelengths than light waves, allowing them to diffract more easily around obstacles.
Factors Affecting Diffraction
Wavelength: Longer wavelengths diffract more than shorter wavelengths.
Aperture Size: Diffraction is more significant when the aperture size is similar to the wavelength.
Common Mistake
Students often confuse diffraction with refraction.
Remember, diffraction occurs when waves bend around obstacles or through openings, while refraction involves bending due to a change in speed across media.
Active recall
State the relationship between a ray and its wavefront.
Write Snell's law and define each quantity in it.
Under what condition does total internal reflection occur?
What happens to a wave's frequency and wavelength when it is transmitted into a slower medium?