Physics · Grades 9–12
Refraction and critical conditions
Track speed, wavelength and angle while frequency stays tied to the source.
Learn the idea
Index
Refractive index relates vacuum light speed to speed in a medium: n = c/v.
Frequency
At a stationary boundary the transmitted wave keeps the source frequency while speed and wavelength may change.
Snell's law
n₁ sin θ₁ = n₂ sin θ₂, with angles from the normal.
Total internal reflection
It requires travel from higher to lower refractive index and incidence above the critical angle. Not every boundary crossing can produce it.
Worked examples
Use c = 300 million m/s. A medium has n = 1.5. Find speed in million m/s.
300/1.5 = 200 million m/s.
200
At a stationary boundary, which property of transmitted light remains unchanged?
The source frequency is maintained while speed and wavelength can change.
Frequency
Check your understanding
For total internal reflection, light must first travel in which direction?
- Only between equal indices
- Higher index toward lower index
- Lower index toward higher index
Light passes from n₁ = 1 to n₂ = 2 with sin θ₁ = 0.6. Find sin θ₂.
Why does light entering a higher-index medium at a nonzero incidence angle generally bend toward the normal?
Answers and marking notes
Answers and marking notes
- Higher index toward lower index
The critical-angle condition requires the initial index to be larger.
- 0.3
Snell's law gives 1 × 0.6 / 2 = 0.3.
- Its speed is lower and Snell's law gives a smaller angle to the normal.
Credit a correct index-angle relationship without copying a memorized sketch.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Independent educational review required. Grade bands are approximate; these are not officially aligned curricula.