This cheat sheet covers how light bends when it passes between materials and how lenses use refraction to form images. Students need these ideas to solve problems involving glass, water, prisms, eyeglasses, and optical instruments. Worked examples help connect formulas to real physical situations.
The focus is on using the correct equation, units, and angle measurements.
Key Facts
- Refractive index is defined by , where is the speed of light in vacuum and is the speed of light in the material.
- Snell's law is , where angles are measured from the normal line.
- When light enters a higher refractive index material, it bends toward the normal, so if .
- When light enters a lower refractive index material, it bends away from the normal, so if .
- The critical angle is found from when light travels from a higher index medium into a lower index medium.
- Total internal reflection occurs only when and the incident angle satisfies .
- Lens power is , where is measured in diopters and focal length is measured in meters.
- A converging lens has positive focal length and positive power, while a diverging lens has negative focal length and negative power.
Vocabulary
- Refraction
- Refraction is the change in direction of light as it passes from one medium into another because its speed changes.
- Refractive Index
- Refractive index is a number that compares the speed of light in vacuum to the speed of light in a material using .
- Normal Line
- The normal line is an imaginary line drawn perpendicular to the surface where the light ray meets the boundary.
- 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 happens when light in a higher index medium reflects completely at a boundary with a lower index medium.
- Lens Power
- Lens power describes how strongly a lens bends light and is calculated using with in meters.
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 normal line.
- Forgetting to convert focal length to meters gives the wrong lens power because requires in meters.
- Using total internal reflection when light enters a higher index material is wrong because total internal reflection requires light to travel from higher to lower .
- Treating a negative lens power as a calculation error is wrong because diverging lenses have negative focal length and negative power.
- Rounding too early in Snell's law can change the final angle noticeably, so keep several digits until the last step.
Practice Questions
- 1 Light travels from air with into glass with at an incident angle of . Find the refracted angle using Snell's law.
- 2 A lens has focal length . Calculate its power in diopters and state whether it is converging or diverging.
- 3 Light travels from water with into air with . Calculate the critical angle .
- 4 Explain why a ray bends toward the normal when it enters glass from air, using the relationship between light speed and refractive index.
Understanding Refraction and Lens Power Worked Examples
At a boundary, light changes direction because its speed changes unevenly across the advancing wavefront. One side of the wavefront enters the new material first and slows down or speeds up first. That timing difference turns the wavefront, which turns the ray direction.
The light frequency stays the same because it is set by the source. Its wavelength changes instead. This helps explain why the colour of a beam does not suddenly change when it enters water, even though the path changes.
In ray diagrams, draw the normal before measuring any angle. The normal is an imaginary line perpendicular to the surface at the exact point where the ray meets it.
A reliable calculation method prevents many common errors. Identify the material the ray starts in and the material it enters. Label the incident ray before choosing the two refractive indices.
Then decide whether the refracted ray should move closer to the normal or farther from it. This prediction acts as a check on the calculator result. Use degree mode for school refraction problems unless the question clearly states otherwise.
When finding an unknown angle, the final calculator step usually uses inverse sine. Keep extra digits until the end, then round sensibly. Refractive index has no unit, so a unit written beside it often signals that another quantity has been confused with it.
The critical angle marks a boundary between two different outcomes. At exactly this angle, the refracted ray travels along the surface. A slightly larger incident angle produces no transmitted ray into the second material.
Instead, the light reflects completely back into the first material. This effect keeps light trapped inside optical fibres, which carry signals through long cables. It contributes to the bright flashes seen in cut gemstones.
In diagrams, total internal reflection is only possible when the ray approaches the boundary from the optically denser material. A ray travelling from air into glass cannot produce this effect at that boundary, regardless of its angle.
Lens power describes how strongly a lens changes the paths of nearby rays. It is not a direct measure of lens size. A lens with a focal length of one half metre has a power of two diopters.
A lens with a focal length of one quarter metre has a power of four diopters. Halving focal length therefore doubles power. Stronger lenses usually have more curved surfaces, though lens material matters too.
In eyeglass prescriptions, a positive value corrects long sight by bringing rays together sooner. A negative value corrects short sight by spreading rays before the eye focuses them. When using image diagrams, trace a ray parallel to the main axis and a ray through the lens centre.
Their intersection gives the image position for a thin converging lens. Follow the sign convention used by your course carefully, since textbooks can present image distances in different ways.