Physics Exam Reviewer: Light, Reflection, and Refraction Study Guide

Fundamental Concepts and Definitions

• Reflection: The bouncing back of light waves when striking a surface boundary.
• Refraction: The bending of light passing from one medium into another of different optical density.
• Normal Line: An imaginary line drawn perpendicular ($90^\circ$) to the surface at the point of incidence.
• Incident Ray: An incoming ray of light that strikes at the surface boundary.
• Reflective Ray: A ray of light that bounces off the surface and travels away.
• Refracted Ray: A ray of light that passes into a second medium and undergoes a change in direction.
• Angle of Incidence ($\theta_i$): The angle between the incident ray and the normal line.
• Angle of Reflection ($\theta_r$): The angle between the reflected ray and the normal line.
• Angle of Refraction: The angle between the refracted ray and the normal line.
• Fastest Phenomenon in the Universe: Light traveling in a vacuum.
• Speed of Light in Vacuum ($c$): $c = 3.0 \times 10^8\,\text{m/s}$.

Types of Light Rays

• Parallel Rays: Light rays that travel parallel to each other and never intersect.
• Converging Rays: Light rays that move toward each other to meet at a single point.
• Diverging Rays: Light rays that move outward from a single point.

Classifications of Optical Media

• Transparent Medium: A medium where light passes through without being scattered or blocked.
  • Examples: Clear glass, Water, Air, Clear plastic wrap, Diamond.
• Translucent Medium: A medium where light partly passes through but scatters, causing objects seen through it to appear blurry.
  • Examples: Tinted glass, Frosted glass, Wax paper, Butter paper, Tissue paper.
• Opaque Medium: A medium where light cannot pass through; it absorbs or reflects all incoming light.
  • Examples: Book, Wood, Metal, Cardboard, Brick.

Optical Diagrams and Governing Principles

Reflection Diagram and Principles

• Key Components of Reflection:
  • Surface / Mirror reflection boundary.
  • Normal line drawn perpendicular ($90^\circ$) to the surface.
  • Incident ray making an angle of incidence ($\theta_1$ or $\theta_i$) with the normal line.
  • Reflected ray making an angle of reflection ($\theta_2$ or $\theta_r$) with the normal line.
  • Law of Reflection: The angle of incidence is equal to the angle of reflection ($\theta_1 = \theta_2$).

Refraction Diagrams and Principles

• Key Components of Refraction:
  • Surface boundary separating Substance 1 (Air / Rarer Medium) and Substance 2 (Glass or Water / Denser Medium).
  • Normal line drawn perpendicular ($90^\circ$) across the interface.
  • Angle of incidence ($i$ or $\theta_i$) measured between the incident ray and the normal line in the initial medium.
  • Angle of refraction ($r$ or $\theta_r$) measured between the refracted ray and the normal line in the secondary medium.
  • Physical Manifestation: A straight pencil immersed in water appears bent at the air-water interface due to light changing speed and direction upon crossing optical media.

Mathematical Formulas of Optics

• Snell's Law Formula:   $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$

  • $n_1$ = Index of refraction of medium 1
  • $\theta_1$ = Angle of incidence in medium 1
  • $n_2$ = Index of refraction of medium 2
  • $\theta_2$ = Angle of refraction in medium 2

• Refractive Index Formula:   $n = \frac{c}{v}$

  • $n$ = Index of refraction (dimensionless quantity)
  • $c$ = Speed of light in vacuum ($3.0 \times 10^8\,\text{m/s}$)
  • $v$ = Speed of light in the specified medium ($\text{m/s}$)

• Speed of Light in Medium Formula:   $v = \frac{c}{n}$

Data Table: Index of Refraction and Speed of Light

• Example Instance:
  • Diamond has an Index of Refraction $n = 2.42$ and a Speed of Light $v = 1.25 \times 10^8\,\text{m/s}$.

Critical Problem-Solving Terminology Rules

• Keyword Rule 1 ("STRIKES with THE SURFACE"): Indicates the angle given is measured with respect to the physical surface boundary (the glancing angle).
  • To calculate the true Angle of Incidence ($\theta_i$):     $\theta_i = 90^\circ - \text{glancing angle}$
• Keyword Rule 2 ("STRIKES with THE NORMAL"): Indicates the angle given is measured directly with respect to the normal line.
  • The given angle is equal to the Angle of Incidence ($\theta_i$):     $\theta_i = \text{given angle}$

Reflection Problem Solving

Problem 1: Light ray strikes mirror at $30^\circ$ with the surface

• Calculations:
  • A. Angle of Incidence ($\theta_i$):     $\theta_i = 90^\circ - 30^\circ = 60^\circ$
  • B. Angle of Reflection ($\theta_r$):     $\theta_r = 60^\circ$
  • C. Angle with Mirror Surface:     $\text{Angle with mirror surface} = 30^\circ$
  • D. Angle Between Rays:     $\text{Angle between incident and reflected rays} = 60^\circ + 60^\circ = 120^\circ$

Problem 2: Light ray strikes mirror at $54^\circ$ with the surface

• Calculations:
  • A. Angle of Incidence ($\theta_i$):     $\theta_i = 90^\circ - 54^\circ = 36^\circ$
  • B. Angle of Reflection ($\theta_r$):     $\theta_r = 36^\circ$
  • C. Angle with Mirror Surface:     $\text{Angle with mirror surface} = 54^\circ$
  • D. Angle Between Rays:     $\text{Angle between incident and reflected rays} = 36^\circ + 36^\circ = 72^\circ$

Problem 3: Light ray strikes mirror at $40^\circ$ with the normal

• Calculations:
  • A. Angle of Incidence ($\theta_i$):     $\theta_i = 40^\circ$
  • B. Angle of Reflection ($\theta_r$):     $\theta_r = 40^\circ$
  • C. Angle with Mirror Surface:     $\text{Angle with mirror surface} = 90^\circ - 40^\circ = 50^\circ$
  • D. Angle Between Rays:     $\text{Angle between incident and reflected rays} = 40^\circ + 40^\circ = 80^\circ$

Problem 4: Corner Reflector System

• Parameters:
  • Corner reflector formed by two perpendicular mirrors where angle $\alpha = 90^\circ$.
• Mechanism & Path Explanation:
  • Two perpendicular mirrors ($90^\circ$) reflect light twice so that the final reflected ray leaves at $180^\circ$ relative to its original path, making it parallel to the incident ray.

Refractive Index and Speed of Light Problem Solving

• Standard Constant: Speed of light in vacuum $c = 3.0 \times 10^8\,\text{m/s}$.

Problem 5: Index of Refraction of Alcohol

• Given: Speed of light in alcohol $v = 2.21 \times 10^8\,\text{m/s}$.
• Formula:   $n = \frac{c}{v}$
• Substitution:   $n = \frac{3.0 \times 10^8\,\text{m/s}}{2.21 \times 10^8\,\text{m/s}}$
• Result:   $n = 1.36$

Problem 6: Speed of Light in Water

• Given: Index of refraction of water $n = 1.33$.
• Formula:   $v = \frac{c}{n}$
• Substitution:   $v = \frac{3.0 \times 10^8\,\text{m/s}}{1.33}$
• Result:   $v = 2.26 \times 10^8\,\text{m/s}$

Problem 7: Speed of Light in Glass

• Given: Index of refraction of glass $n = 1.50$.
• Formula:   $v = \frac{c}{n}$
• Substitution:   $v = \frac{3.0 \times 10^8\,\text{m/s}}{1.50}$
• Result:   $v = 2.00 \times 10^8\,\text{m/s}$

Problem 8: Speed of Light in Diamond

• Given: Index of refraction of diamond $n = 2.42$.
• Formula:   $v = \frac{c}{n}$
• Substitution:   $v = \frac{3.0 \times 10^8\,\text{m/s}}{2.42}$
• Result:   $v = 1.24 \times 10^8\,\text{m/s}$