AcademyGeometric Optics
Academy
Plane-Surface Refraction
Level 1 - Physics topic page in Geometric Optics.
Principle
Refraction changes ray direction because light speed changes at a boundary.
Notation
\(n\)
index of refraction
1
\(v\)
speed of light in a medium
\(\mathrm{m\,s^{-1}}\)
\(\theta_1\)
incident angle from the normal
\(\mathrm{rad}\)
\(\theta_2\)
refracted angle from the normal
\(\mathrm{rad}\)
\(\lambda\)
wavelength in the medium
\(\mathrm{m}\)
\(f\)
light frequency
\(\mathrm{Hz}\)
Method
Derivation 1: Index and speed
The refractive index compares vacuum light speed with the speed in a medium.
Index definition
\[n=\frac{c}{v}\]
Medium speed
\[v=\frac{c}{n}\]
Derivation 2: Snell's law
Frequency is continuous across a boundary. The wavelength changes with speed, changing the ray direction.
Boundary law
\[n_1\sin\theta_1=n_2\sin\theta_2\]
Wavelength in medium
\[\lambda=\frac{\lambda_0}{n}\]
Frequency unchanged
\[f_1=f_2\]
Rules
Refractive index
\[n=\frac{c}{v}\]
Snell's law
\[n_1\sin\theta_1=n_2\sin\theta_2\]
Medium wavelength
\[\lambda=\lambda_0/n\]
Examples
Question
Light goes from air into glass
\[(n=1.50)\]
at \[30^\circ\]
Find the refracted angle.Answer
\[1.00\sin30^\circ=1.50\sin\theta_2\]
\[\theta_2=19.5^\circ\]
Checks
- Entering a larger \(n\) bends a ray toward the normal.
- Frequency does not change at a boundary.
- Wavelength and speed change in the same ratio.