AcademyLight Propagation
Academy
Reflection and Refraction
Level 1 - Physics topic page in Light Propagation.
Principle
At a boundary, light can reflect back into the first medium and refract into the second. Reflection preserves the angle to the normal; refraction follows Snell's law.
Notation
\(\theta_i\)
angle of incidence measured from the normal
\(\mathrm{rad}\)
\(\theta_r\)
angle of reflection measured from the normal
\(\mathrm{rad}\)
\(\theta_2\)
angle of refraction measured from the normal
\(\mathrm{rad}\)
\(n_1, n_2\)
refractive indices of the two media
\(v_1, v_2\)
light speeds in the two media
\(\mathrm{m\,s^{-1}}\)
Method
Derivation 1: Apply reflection law
Angles are measured from the normal line, not from the surface.
Reflection law
\[\theta_r=\theta_i\]
Derivation 2: Apply Snell's law
Refraction changes direction because the wave speed changes at the boundary.
Snell's law
\[n_1\sin\theta_1=n_2\sin\theta_2\]
Speed form
\[\frac{\sin\theta_1}{\sin\theta_2}=\frac{v_1}{v_2}\]
Derivation 3: Decide bending direction
Entering a higher-index medium makes light slow down and bend toward the normal. Entering a lower-index medium makes it speed up and bend away from the normal.
Rules
Reflection
\[\theta_r=\theta_i\]
Snell's law
\[n_1\sin\theta_1=n_2\sin\theta_2\]
Speed-index relation
\[v=\frac{c}{n}\]
Frequency across boundary
\[f_1=f_2\]
Examples
Question
A light ray hits a plane mirror at
\[35^\circ\]
to the normal. Find the reflection angle.Answer
The reflection angle is measured from the normal and equals the incidence angle:
\[35^\circ\]
Checks
- Measure all optical angles from the normal.
- Higher refractive index means lower light speed.
- Bending toward the normal means the angle gets smaller.
- Refraction changes wavelength, not frequency.