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Reflection & Refraction
Snell's Law, Critical Angle, and Total Internal Reflection
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Reflection and refraction describe what happens when light reaches the boundary between two different media. Some of the light can bounce back into the original medium, which is reflection, while some can pass into the new medium and change direction, which is refraction. These ideas are essential for understanding mirrors, lenses, eyeglasses, cameras, and many natural optical effects. Snell's law gives the mathematical rule that predicts how much a light ray bends.
The key to both processes is the boundary and the normal line drawn perpendicular to it. The angle of reflection always equals the angle of incidence, but the refracted angle depends on the refractive indices of the two media. When light enters a medium where it travels more slowly, it bends toward the normal, and when it enters a medium where it travels faster, it bends away from the normal. This behavior helps explain image formation in lenses, fiber optics, and why objects under water appear shifted.
Key Facts
- Law of reflection: theta_r = theta_i
- Snell's law: n1 sin(theta1) = n2 sin(theta2)
- Refractive index: n = c/v
- If n2 > n1, the refracted ray bends toward the normal
- If n2 < n1, the refracted ray bends away from the normal
- Critical angle for total internal reflection: sin(theta_c) = n2/n1, for n1 > n2
Vocabulary
- Incident ray
- The incoming light ray that strikes a boundary between two media.
- Normal
- An imaginary line perpendicular to the surface at the point where the ray hits.
- Reflection
- The bouncing of light back into the original medium after hitting a surface.
- Refraction
- The bending of light as it passes from one medium into another with a different refractive index.
- Refractive index
- A number that shows how much light slows down in a material compared with its speed in vacuum.
Common Mistakes to Avoid
- Measuring angles from the surface instead of from the normal, which gives the wrong values for both reflection and refraction calculations. Always measure every ray angle relative to the perpendicular line.
- Assuming light always bends toward the normal, which is wrong because the direction depends on the refractive indices of the two media. Light bends away from the normal when it enters a lower index medium.
- Using Snell's law with the indices or angles swapped, which leads to incorrect answers. Match n1 with theta1 in the first medium and n2 with theta2 in the second medium.
- Thinking reflected and refracted rays are the same process, which hides the fact that one ray stays in the original medium and the other enters a new medium. Keep track of which side of the boundary each ray occupies.
Practice Questions
- 1 A light ray travels from air with n1 = 1.00 into glass with n2 = 1.50 at an incident angle of 30 degrees. Find the refracted angle.
- 2 A ray in water with n1 = 1.33 strikes an air boundary with an incident angle of 40 degrees. Calculate the refracted angle in air.
- 3 A light ray goes from glass into air and bends away from the normal. Explain what this tells you about the relative refractive indices and the speed of light in the two media.