Chapter 14: Refraction

Overview

• Understanding refraction and its occurrences.
• Recognizing the direction of light bending between media.
• Solving problems using Snell's Law.

Key Concepts

What is Refraction?

• Refraction: Bending of light as it travels from one medium to another.
• Wavelength Dependency: Refraction depends on the wavelength of light.
• Formation of Rainbows: Different wavelengths bend at different angles, causing dispersion of light into a spectrum.
• Visual Effects in Water: Objects like a pencil in a cup appear misaligned due to refraction.

Angle of Incidence and Refraction

• Angle of Incidence: Measured from the normal line.
• Angle of Refraction: The angle light changes as it enters a new medium.

Index of Refraction (n)

• Formula: Ratio of speed of light in vacuum to speed in medium.
• Greater than One: Because light travels faster in a vacuum.
• Direction of Bending:
  • From lower to higher n, light bends towards the normal.
  • From higher to lower n, light bends away from the normal.

Refraction and Perception

• Perception of objects in water is altered due to refraction.
• Example: A cat sees a fish closer than it appears because of light bending in water.

Snell’s Law

• Formula: ( n_1 \cdot \sin(\theta_1) = n_2 \cdot \sin(\theta_2) )
  • ( n_1, n_2 ) are indices of refraction for the two media.
  • ( \theta_1 ), ( \theta_2 ) are the angles of incidence and refraction.
• Example Problem:
  1. Light enters water from air at a 25-degree angle.
  2. Index of refraction for air is 1.0, for water is 1.33.
  3. Calculate the angle of refraction using Snell's Law:
     • Rearrange formula: ( \sin^{-1}\left(\frac{\sin(25)}{1.33}\right) = \theta_r ).
  4. Result: Angle of refraction ( \theta_r ) is 18 degrees.
  5. Ensure calculator is in degree mode to avoid errors.

Conclusion

• Refraction is crucial in understanding how light behaves across different media.
• Use of Snell’s Law allows precise calculations of angles of refraction.
• Important for various applications such as optics, physics studies, and understanding natural phenomena like rainbows.