Kylie Science M.3

Types of Medium

1. Transparent

2. Translucent

3. Opaque

Snell's Law Formula

$$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$$

Normal Line

An imaginary line drawn perpendicular ($90^\circ$) to the surface at the point of incidence.

Angle of Reflection

The angle between the reflected ray and the normal line.

Angle of Incidence

The angle between the incident ray and the normal line.

Reflection

The bouncing back of light waves when striking a surface boundary.

Refraction

The bending of light as it passes from one medium into another of different optical density.

Fastest Thing in the Universe

Light (in a vacuum)

Speed of Light in Vacuum ($c$)

$$c = 3.0 \times 10^8\,m/s$$

3 Types of Light Rays

• Parallel rays
• Converging rays
• Diverging rays

Definitions of Parallel, Converging, and Diverging 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 spread outward from a single point.

Transparent Medium

A material that allows light to pass through completely, making objects clearly visible.

Translucent Medium

A material that allows some light to pass through but scatters it, making objects appear blurry.

Opaque Medium

A material that allows no light to pass through; completely absorbs or reflects light.

Incident Ray

The incoming ray of light that strikes the surface boundary.

Reflected Ray

The ray of light that bounces off the surface and travels away.

5 Examples of Transparent Mediums

• Clear glass
• Water
• Air
• Clear plastic wrap
• Diamond

5 Examples of Translucent Mediums

• Tinted glass
• Frosted glass
• Wax paper
• Butter paper
• Tissue paper

5 Examples of Opaque Mediums

• Book
• Wood
• Metal
• Cardboard
• Brick

Index of Refraction Formula

$$n = \frac{c}{v}$$

Problem 1: Ray strikes mirror surface at an angle of $30^\circ$ with the surface. Find: A. Angle of Incidence ($\theta_i$), B. Angle of Reflection ($\theta_r$), C. Angle with the Mirror Surface, D. Angle Between Incident Ray and Reflected Ray.

• A. Angle of Incidence ($\theta_i$) = $90^\circ - 30^\circ = 60^\circ$
• B. Angle of Reflection ($\theta_r$) = $60^\circ$
• C. Angle with Mirror Surface = $30^\circ$
• D. Angle Between Incident and Reflected Rays = $60^\circ + 60^\circ = 120^\circ$

Problem 2: Light strikes reflective plane surface at an angle of $54^\circ$ with the surface. Find: A. Angle of Incidence ($\theta_i$), B. Angle of Reflection ($\theta_r$), C. Angle with the Mirror Surface, D. Angle Between Incident Ray and Reflected Ray.

• A. Angle of Incidence ($\theta_i$) = $90^\circ - 54^\circ = 36^\circ$
• B. Angle of Reflection ($\theta_r$) = $36^\circ$
• C. Angle with Mirror Surface = $54^\circ$
• D. Angle Between Incident and Reflected Rays = $36^\circ + 36^\circ = 72^\circ$

Problem 3: Ray strikes plane mirror making an angle of $40^\circ$ with the normal. Find: A. Angle of Incidence ($\theta_i$), B. Angle of Reflection ($\theta_r$), C. Angle with the Mirror Surface, D. Angle Between Incident Ray and Reflected Ray.

• A. Angle of Incidence ($\theta_i$) = $40^\circ$
• B. Angle of Reflection ($\theta_r$) = $40^\circ$
• C. Angle with Mirror Surface = $90^\circ - 40^\circ = 50^\circ$
• D. Angle Between Incident and Reflected Rays = $40^\circ + 40^\circ = 80^\circ$

Problem 4: Find angle $\alpha$ made by a system of two mirrors so that an incident ray at mirror A and reflected ray at mirror B are parallel.

$\alpha = 90^\circ$ Explanation: When two plane mirrors meet at a $90^\circ$ angle (corner reflector), any incoming ray striking both mirrors reflects back parallel to its incoming direction.

Formulas: Index of Refraction and Speed of Light

• Index of Refraction: $n = \frac{c}{v}$
• Speed of Light in Medium: $v = \frac{c}{n}$
• Speed of Light in Vacuum: $c = 3.0 \times 10^8\,m/s$

Index of Refraction Problem #1: The speed of light in alcohol is $2.21 \times 10^8\,m/s$. What is its index of refraction?

• Given: $c = 3.0 \times 10^8\,m/s$, $v = 2.21 \times 10^8\,m/s$
• Formula: $n = \frac{c}{v}$
• Calculation: $n = \frac{3.0 \times 10^8}{2.21 \times 10^8} = 1.357$
• Answer: $n = 1.36$

Index of Refraction Problem #2: The index of refraction of water is $1.33$. What is the speed of light in water?

• Given: $c = 3.0 \times 10^8\,m/s$, $n = 1.33$
• Formula: $v = \frac{c}{n}$
• Calculation: $v = \frac{3.0 \times 10^8}{1.33} = 2.2556 \times 10^8\,m/s$
• Answer: $v = 2.26 \times 10^8\,m/s$ (Table value: $2.25 \times 10^8\,m/s$)

Index of Refraction Problem #3: The index of refraction of glass is approximately $1.50$. What is the speed of light in glass?

• Given: $c = 3.0 \times 10^8\,m/s$, $n = 1.50$
• Formula: $v = \frac{c}{n}$
• Calculation: $v = \frac{3.0 \times 10^8}{1.50} = 2.00 \times 10^8\,m/s$
• Answer: $v = 2.00 \times 10^8\,m/s$

Index of Refraction Problem #4: Diamond has an index of refraction of $2.42$. Calculate the speed of light in diamond.

• Given: $c = 3.0 \times 10^8\,m/s$, $n = 2.42$
• Formula: $v = \frac{c}{n}$
• Calculation: $v = \frac{3.0 \times 10^8}{2.42} = 1.2396 \times 10^8\,m/s$
• Answer: $v = 1.24 \times 10^8\,m/s$ (Table value: $1.25 \times 10^8\,m/s$)