Snell's Law describes how light bends when it passes from one material into another, such as from air into glass or water. This cheat sheet helps students connect ray diagrams, angles, refractive index, and wave speed in one organized reference. It is useful for solving refraction problems, predicting whether light bends toward or away from the normal, and recognizing total internal reflection.
Key Facts
- Snell's Law is , where angles are measured from the normal.
- The refractive index is , where is the speed of light in vacuum and is the speed of light in the material.
- When light enters a higher-index material, , it slows down and bends toward the normal, so .
- When light enters a lower-index material, , it speeds up and bends away from the normal, so .
- The critical angle is found from when light travels from a higher-index material to a lower-index material.
- Total internal reflection occurs only when and the incident angle is greater than the critical angle, .
- At the critical angle, the refracted ray travels along the boundary, so .
- Frequency stays the same during refraction, but speed and wavelength change according to .
Vocabulary
- Refraction
- Refraction is the bending of light as it changes speed when moving from one medium into another.
- Refractive Index
- Refractive index measures how much a material slows light compared with its speed in vacuum.
- Normal
- The normal is an imaginary line drawn perpendicular to the surface where the light ray hits.
- Incident Angle
- The incident angle is the angle between the incoming ray and the normal.
- Critical Angle
- The critical angle is the incident angle that makes the refracted ray travel along the boundary at .
- Total Internal Reflection
- Total internal reflection is the complete reflection of light inside a higher-index medium when the incident angle exceeds the critical angle.
Common Mistakes to Avoid
- Measuring angles from the surface instead of the normal is wrong because Snell's Law uses angles measured from the perpendicular line to the boundary.
- Using total internal reflection when light goes from air into glass is wrong because total internal reflection requires light to travel from higher to lower .
- Forgetting to check before calculating a critical angle is wrong because only applies in that direction.
- Assuming light always bends toward the normal is wrong because light bends away from the normal when it enters a lower-index medium.
- Rounding too early in Snell's Law calculations is wrong because small angle errors can change whether is above or below .
Practice Questions
- 1 Light travels from air with into glass with at an incident angle of . Use to find .
- 2 Light travels from water with into air with . Find the critical angle using .
- 3 A ray inside glass with strikes a glass-air boundary at . If the critical angle is about , determine whether total internal reflection occurs.
- 4 Explain why optical fibers can guide light around bends, and identify the two conditions needed for total internal reflection.
Understanding Snell's Law & Total Internal Reflection
Refraction is easier to understand by thinking about a line of wavefronts instead of a single ray. When one side of a wavefront reaches a new material first, that side changes speed first. The other side keeps moving at its earlier speed for a short time.
This difference makes the wavefront rotate. A ray, which shows the direction of energy travel, changes direction because it stays perpendicular to the rotating wavefront.
This model explains why the change happens right at the boundary. It also shows that bending is caused by a speed change, not because the boundary pulls on light.
The source of the light sets its frequency. A material cannot change that frequency at its surface because the incoming wave must match the wave in the new material at every moment. Since the speed changes while frequency remains fixed, the spacing between wave peaks must change.
That spacing is the wavelength. Shorter wavelengths occur in a material where light travels more slowly. This matters for color effects.
Different colors have slightly different refractive indices in many transparent materials. Blue light usually bends more than red light, which is why a prism can spread white light into a spectrum.
Total internal reflection is not simply ordinary reflection from a shiny surface. It happens when no traveling light wave can continue into the second material at the required direction. The boundary sends the light back into the first material.
Small amounts of energy can still exist just beyond the boundary in a very thin region. This is called an evanescent wave. It does not carry light away in the usual direction.
The effect is strongest with clean, smooth boundaries. Dust, scratches, bends, or contact with another material can allow some light to escape.
Optical fibers use repeated total internal reflection to guide light through long flexible strands of glass. The central core has a slightly higher refractive index than the surrounding cladding. This keeps signals inside the core over large distances.
Fibers carry internet data, medical camera images, and signals in sensors. Prisms in binoculars and some cameras use internal reflection to turn light paths without relying on metal mirrors. In calculations, first identify the medium where the ray begins and the medium it enters.
Draw the normal at the exact point where the ray meets the boundary. Measure every angle from that normal, not from the surface. Then check whether transmission is possible before trying to calculate a refracted angle.
At the critical condition, the outgoing ray skims along the boundary. Beyond that condition, only reflection remains.