🔖 Topics

  • Geometric optics
  • Reflection
  • Plane mirrors
  • Refraction
  • Total internal reflection
  • Apparent depth

🎯 Objectives

  • Describe the path that light takes as it travels within and between homogeneous media
  • Utilize Snell's law to calculate how much light "bends" at an interface
  • Calculate the angle at which total internal reflection occurs
  • Solve a variety of problems related to geometric optics

📋 Sequence

  • Wavefronts
  • Huygen’s Principle
  • Reflection by a Plane Mirror
    • Example: Two Plane Mirrors at \( 90^\circ \)
    • Example: Minimum Height of a Plane Mirror
  • Refraction of Light
    • Example: Snell’s Law at a Surface
    • Example: Snell’s Law in a Thin Film
  • Total Internal Reflection
    • Example: Water / Air TIR
  • Apparent Depth
    • Example: Water / Air Apparent Depth of Fish

🖥️ Animations, Simulations, Activities

📝 Practice Problems

  1. The index of water is 1.33. What is the speed of light in water? What is the wavelength of light in water if it has a vacuum wavelength of 515 nm?
  2. Unpolarized light is incident on a system of three ideal polarizers. The second polarizer is oriented at an angle of \( 30^\circ \) with respect to the first, and the third is oriented with an angle of \( 45^\circ \) with respect to the first. If light exits the system of polarizers with an intensity of \( 23 \: W/m^2 \), what is the intensity of the incident light?
  3. Two plane mirrors form a \( 70^\circ \) angle as shown in the diagram. For what angle \( \theta \) will the outgoing ray be horizontal?

Two Plane Mirrors

  1. A ray of light strikes an air / water interface at an angle of \( 25^\circ \) with respect to the vertical. At what angle, with respect to the vertical, will the light move through the water? The index of refraction of water is 1.33.
  2. A glass lens has a scratch-resistant plastic coating on it. The speed of light in the glass is 0.67c and the speed of light in the coating is 0.80c. A ray of light in the coating is incident on the plastic-glass boundary at an angle of \( 12^\circ \) with respect to the normal. At what angle with respect to the normal is the ray transmitted into the glass?
  3. Calculate the critical angle for sapphire surrounded by air. The index of refraction for sapphire is 1.76.
  4. A defect in diamond appears to be 2.0 mm below the surface. If the index of refraction of diamond is 2.42, how far below the surface is the defect actually located?
  5. Why does a diamond sparkle less under water than in air?

Challenge Problem

A horizontal light ray is incident on a crown glass prism as shown in the figure. The angle \( \beta = 30^\circ \) and the index of refraction of the crown glass is n = 1.50. Calculate \( \delta \), also called the angle of deviation.

Crown Glass Prism

✅ Partial Solutions

  1. \( 2.26 \times 10^8 : m/s \); \( 387.2 \: nm \)
  2. \( 65.7 \: W/m^2 \)
  3. \( 40^\circ \)
  4. \( 18.5^\circ \)
  5. \( 10^\circ \)
  6. \( 34.6^\circ \)
  7. 4.84 mm

📘 Connected Resources

  • Giambattista, Alan, et al. College Physics With an Integrated Approach to Forces and Kinematics. 5th ed., McGraw-Hill Education, 2020.