Lecture on the Law of Reflection and Refraction

Key Concepts

1. Law of Reflection

• Incident Ray: The ray that strikes a surface.
• Reflected Ray: The ray that bounces off the surface.
• Angle of Incidence: The angle between the incident ray and the normal line.
• Angle of Reflection: The angle between the reflected ray and the normal line.
• Law of Reflection: The angle of incidence equals the angle of reflection.

2. Law of Refraction

• Refraction: Bending of light as it passes from one medium to another.
• Refracted Ray: The ray that is bent as it enters a new medium.
• Angle of Refraction: The angle between the refracted ray and the normal line.
• Snell's Law: ( n_1 \sin \theta_1 = n_2 \sin \theta_2 ) where:
  • ( n_1 ), ( n_2 ) are indices of refraction for the two media.
  • ( \theta_1 ), ( \theta_2 ) are the angles of incidence and refraction respectively.
• As light moves from a lower to a higher index of refraction, it bends towards the normal line.

Index of Refraction

• Measures how much light bends when entering a new medium.
• Air: ( n \approx 1 )
• Glass: ( n \approx 1.5 )
• Diamond: ( n \approx 2.4 )
• Calculation Example: Use Snell's Law to find angles.

Speed of Light in Different Media

• Speed of Light in Vacuum: ( 3 \times 10^8 \text{ m/s} )
• Equation: ( v = \frac{c}{n} ) where:
  • ( v ) is the speed of light in the material.
  • ( c ) is the speed of light in vacuum.
  • ( n ) is the index of refraction.
• Light travels slower in materials like water and glass compared to vacuum.

Wavelength Changes

• Equation: ( \frac{\lambda_2}{\lambda_1} = \frac{n_1}{n_2} )
• Wavelength decreases as the index of refraction increases.
• Frequency remains constant even as wavelength and speed change.

Reflection Types

• Diffuse Reflection: Occurs on rough surfaces; light scatters.
• Specular Reflection: Occurs on smooth surfaces; clear image as light does not scatter.

Practice Problems

1. Finding Angles on Mirrors
   • Use geometry and the law of reflection to find angles.
2. Light Passing Through Multiple Media
   • Use Snell's Law iteratively or directly to find refraction angles.
3. Calculate Speed in Ice
   • Use the speed of light equation to find the index of refraction.
4. Wavelength Change in Diamond
   • Use the wavelength equation to find changes when light enters different media.

Problem-Solving Strategies

• Simplify problems by focusing on initial and final media.
• Use given indices and angles to apply Snell's Law.
• Convert units as necessary (e.g., nm to m).