Solved 3) Law of reflection (35 points) a. [10 points) On | Chegg.com - Free Printable

I'll help you solve this law of reflection problem step by step.

## Part (a): Single Mirror Reflection

For a single mirror with an incident ray:

i. The Normal:
- Draw a dashed line perpendicular (at 90°) to the mirror surface at the point where the incident ray hits the mirror
- Label it "N" or "Normal"

ii. The Reflected Ray:
- According to the law of reflection: angle of incidence = angle of reflection
- Draw the reflected ray on the opposite side of the normal, making sure it makes the same angle with the normal as the incident ray does
- Add an arrow pointing away from the mirror
- Label it "Reflected Ray"

iii. Angles:
- Angle of incidence (θᵢ): The angle between the incident ray and the normal
- Angle of reflection (θᵣ): The angle between the reflected ray and the normal
- Mark both angles with arcs and label them "θᵢ" and "θᵣ" respectively
- These two angles should be equal

## Part (b): Two-Mirror Combinations

For each case, follow these steps:

1. First mirror hit: Draw the normal at the first point of contact, then reflect using θᵢ = θᵣ
2. Second mirror hit: Draw the normal at the second point of contact, then reflect again using θᵢ = θᵣ
3. Continue the path showing all reflections

Case (a): Horizontal ray hitting angled mirror, then reflecting to another angled mirror below
- First reflection: Ray reflects downward at equal angle
- Second reflection: Ray reflects back upward/leftward

Case (b): Horizontal ray entering V-shaped mirrors (opening to left)
- First reflection off bottom mirror: Ray reflects upward
- Second reflection off top mirror: Ray reflects horizontally to the right (parallel to incoming)

Case (c): Diagonal ray entering V-shaped mirrors (opening to left)
- First reflection: Calculate based on incident angle
- Second reflection: Follows law of reflection again

Case (d): Horizontal ray entering V-shaped mirrors (opening to right)
- First reflection off top mirror: Ray reflects downward
- Second reflection off bottom mirror: Ray reflects horizontally to the left

Case (e): Diagonal ray entering V-shaped mirrors (opening to right)
- Similar process with different initial angle

Key Principle for All Cases:
- At EACH mirror surface, draw a normal line perpendicular to that surface
- Measure the angle between the incoming ray and the normal (angle of incidence)
- Draw the outgoing ray at the SAME angle on the other side of the normal (angle of reflection)
- Repeat for each mirror the ray encounters

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Final Answer:

Part (a):
- Draw a perpendicular normal line at the point of incidence
- Draw reflected ray making equal angle with normal on opposite side
- Label both angles of incidence and reflection (they are equal)

Part (b): For all five cases (a-e), trace the light path by:
1. Drawing normals at each mirror contact point
2. Applying θᵢ = θᵣ at each reflection
3. Using straight edge for accuracy
4. Showing complete path through both mirrors