Ray Model of Light - Comprehensive Study Notes

Key Concepts

The Ray Model of Light

Light travels in straight lines called rays, represented by arrows showing the direction of light travel
A light ray is a narrow beam of light that shows the path light takes
A beam of light is a collection of light rays (can be parallel, converging, or diverging)
Light travels at approximately 300,000,000 m/s (3 × 10⁸ m/s) in air/vacuum
The ray model helps us understand how light behaves when it hits surfaces or passes through different materials

Reflection of Light

Reflection occurs when light bounces off a surface
All reflection follows two fundamental laws:
- First Law: The incident ray, reflected ray, and normal all lie in the same plane
- Second Law: The angle of incidence equals the angle of reflection (i = r)
The normal is an imaginary line drawn perpendicular (90°) to the surface at the point of incidence
The angle of incidence (i) is measured between the incident ray and the normal
The angle of reflection ® is measured between the reflected ray and the normal
Important: Angles are ALWAYS measured from the normal, NOT from the surface

Types of Reflection

Regular (specular) reflection: Occurs on smooth surfaces (like mirrors); reflected rays are parallel, producing clear images
Diffuse (irregular) reflection: Occurs on rough surfaces; reflected rays scatter in many directions, no clear image formed

Refraction of Light

Refraction is the bending of light as it passes from one medium to another due to change in speed
Light slows down when entering a denser medium (air → glass) and speeds up when entering a less dense medium (glass → air)
When light enters a denser medium, it bends towards the normal (angle of refraction < angle of incidence)
When light enters a less dense medium, it bends away from the normal (angle of refraction > angle of incidence)
The refractive index (n) measures how much a medium slows down light compared to vacuum
Air has refractive index ≈ 1.0, water ≈ 1.33, glass ≈ 1.5

Snell’s Law

Snell’s Law relates the angles and refractive indices: n₁ sin i = n₂ sin r
- n₁ = refractive index of first medium
- i = angle of incidence
- n₂ = refractive index of second medium
- r = angle of refraction
For light entering from air (n₁ ≈ 1): sin i = n sin r or n = sin i / sin r

Total Internal Reflection

Total internal reflection (TIR) occurs when light traveling in a denser medium hits the boundary with a less dense medium at an angle greater than the critical angle
All light is reflected back into the denser medium; NO light is refracted out
Conditions for TIR:
1. Light must travel from denser to less dense medium
2. Angle of incidence must be greater than the critical angle
Critical angle ©: The angle of incidence in the denser medium for which the angle of refraction is exactly 90°
Formula: sin c = n₂/n₁ (where n₁ > n₂)
For glass-air boundary: critical angle ≈ 42°
For water-air boundary: critical angle ≈ 49°
Applications: Optical fibers, periscopes, binoculars, prisms in cameras

Plane Mirrors

A plane mirror is a flat, smooth reflecting surface
Characteristics of images in plane mirrors:
- Image is virtual (cannot be formed on a screen; appears behind the mirror)
- Image is laterally inverted (left appears right and vice versa)
- Image is upright (same orientation as object)
- Image is the same size as the object (magnification = 1)
- Image distance behind mirror equals object distance in front of mirror
Virtual image: Formed where light rays appear to come from but don’t actually pass through

Curved Mirrors - Introduction

Concave Mirrors (Converging)

A concave mirror curves inward (like the inside of a spoon)
Also called a converging mirror because parallel rays converge (meet) at a point
Principal axis: The horizontal line passing through the center of the mirror
Pole (P): The center point of the mirror surface
Center of curvature ©: The center of the sphere from which the mirror is taken
Radius of curvature ®: Distance from pole to center of curvature
Principal focus (F): Point where parallel rays converge after reflection
Focal length (f): Distance from pole to principal focus; f = r/2
Can produce real images (inverted, can be projected) or virtual images (upright, magnified)
Uses: Shaving mirrors, makeup mirrors, satellite dishes, torch reflectors

Convex Mirrors (Diverging)

A convex mirror curves outward (like the back of a spoon)
Also called a diverging mirror because parallel rays diverge (spread out) after reflection
Reflected rays appear to come from the principal focus behind the mirror
Always produces virtual, upright, diminished (smaller) images
Provides a wider field of view than plane mirrors
Uses: Vehicle side mirrors, security mirrors in shops, blind corner mirrors

Lenses

General Lens Properties

A lens is a transparent material (usually glass or plastic) with at least one curved surface
Principal axis: Line passing through the center of the lens
Optical center (O): Center point of the lens
Principal focus (F): Point where parallel rays converge (converging lens) or appear to diverge from (diverging lens)
Focal length (f): Distance from optical center to principal focus

Converging Lenses (Convex)

A converging lens is thicker at the center than at the edges
Also called a convex lens
Parallel rays converge to a real focus point after passing through the lens
Can produce both real and virtual images depending on object position
When object is beyond F: produces real, inverted image
When object is between F and lens: produces virtual, upright, magnified image
Uses: Magnifying glasses, cameras, projectors, human eye, telescopes, microscopes

Diverging Lenses (Concave)

A diverging lens is thinner at the center than at the edges
Also called a concave lens
Parallel rays diverge after passing through; they appear to come from the principal focus
Always produces virtual, upright, diminished images regardless of object position
Uses: Spectacles for short-sightedness (myopia), peepholes in doors, combination with other lenses

Important Definitions

Light ray: A narrow beam of light traveling in a straight line, represented by a line with an arrow showing direction.

Normal: An imaginary line drawn perpendicular (at 90°) to a surface at the point where a light ray strikes it.

Angle of incidence (i): The angle between the incident ray and the normal.

Angle of reflection ®: The angle between the reflected ray and the normal.

Reflection: The bouncing back of light when it strikes a surface.

Refraction: The bending of light as it passes from one medium to another of different optical density.

Refractive index (n): A measure of how much a medium slows down light; the ratio of the speed of light in vacuum to the speed of light in the medium.

Total internal reflection: The complete reflection of light at the boundary between two media when light travels from a denser to a less dense medium at an angle greater than the critical angle.

Critical angle ©: The angle of incidence in the denser medium for which the angle of refraction in the less dense medium is exactly 90°.

Virtual image: An image formed where light rays appear to come from but do not actually pass through; cannot be formed on a screen.

Real image: An image formed where light rays actually converge; can be projected onto a screen.

Lateral inversion: The left-right reversal of an image (what is on the left appears on the right in the image).

Concave mirror: A curved mirror with the reflecting surface curving inward; converges parallel rays.

Convex mirror: A curved mirror with the reflecting surface curving outward; diverges parallel rays.

Principal axis: A horizontal reference line passing through the center of a curved mirror or lens.

Principal focus (F): The point where parallel rays converge after reflection (concave mirror) or refraction (converging lens), or from where they appear to diverge (convex mirror/diverging lens).

Focal length (f): The distance from the pole/optical center to the principal focus.

Converging lens: A lens that is thicker at the center than at the edges; refracts parallel rays to converge at a focus point.

Diverging lens: A lens that is thinner at the center than at the edges; refracts parallel rays so they diverge.

Diagrams and Structures

Diagram 1: Reflection Ray Diagram

How to draw:

Draw a horizontal line representing the reflecting surface
Draw a vertical dashed line (the normal) perpendicular to the surface at the point of incidence
Draw an incident ray approaching the surface and touching it at the normal
Measure the angle from the normal to the incident ray (angle i)
Measure the same angle on the opposite side of the normal
Draw the reflected ray leaving the surface at this angle (angle r)
Mark angles i and r with arc symbols
Add arrows showing direction: toward surface on incident ray, away from surface on reflected ray

Labels needed:

Incident ray
Reflected ray
Normal (dashed line)
Angle of incidence (i)
Angle of reflection ®
Reflecting surface

Diagram 2: Refraction - Air to Glass

How to draw:

Draw a horizontal line representing the boundary between air (top) and glass (bottom)
Shade or label the glass region below
Draw a vertical dashed line (normal) perpendicular to the boundary
Draw an incident ray in air approaching the boundary at an angle
At the boundary, draw the refracted ray bending TOWARDS the normal in glass
Mark angle of incidence (i) in air and angle of refraction ® in glass
Note: r < i (angle in glass is smaller)

Labels needed:

Air (less dense medium)
Glass (denser medium)
Incident ray
Refracted ray
Normal (dashed line)
Angle of incidence (i)
Angle of refraction ®
Boundary

Diagram 3: Refraction - Glass to Air

How to draw:

Draw a horizontal line representing the boundary between glass (top) and air (bottom)
Shade or label the glass region above
Draw a vertical dashed line (normal) perpendicular to the boundary
Draw an incident ray in glass approaching the boundary at an angle
At the boundary, draw the refracted ray bending AWAY from the normal in air
Mark angle of incidence (i) in glass and angle of refraction ® in air
Note: r > i (angle in air is larger)

Diagram 4: Total Internal Reflection

How to draw:

Draw a horizontal boundary with glass above and air below
Draw a normal (dashed line) perpendicular to the boundary
Draw an incident ray in glass hitting the boundary at an angle greater than the critical angle
Draw the reflected ray entirely within the glass, obeying the law of reflection (i = r)
Add a note: “Angle of incidence > critical angle”
Show NO refracted ray in air

Labels needed:

Glass (denser medium)
Air (less dense medium)
Incident ray
Reflected ray
Normal
Angle of incidence > c
“No refracted ray” or “All light reflected”

Diagram 5: Image Formation in Plane Mirror

How to draw:

Draw a vertical line representing the plane mirror
Draw an object (arrow or stick figure) in front of the mirror
Draw at least 2 light rays from the top of the object to the mirror
Show these rays reflecting off the mirror according to the law of reflection
Extend the reflected rays behind the mirror with dashed lines
Where the dashed lines meet, draw the image (same size, upright, behind mirror)
Measure and mark: object distance = image distance

Labels needed:

Object
Image (dashed/different color to show it’s virtual)
Mirror
Object distance
Image distance
Light rays (solid lines in front, dashed behind mirror)

Diagram 6: Concave Mirror Ray Diagram

How to draw:

Draw a concave mirror (curved inward) as a vertical arc
Draw the principal axis as a horizontal line through the center
Mark and label: Pole (P), Principal Focus (F), Center of Curvature ©
F is halfway between P and C
Draw an object (upward arrow) beyond C
Draw 2 key rays from top of object:
- Ray parallel to principal axis → reflects through F
- Ray through F → reflects parallel to principal axis
Where these rays meet, draw the image (inverted, between F and C)

Labels needed:

Principal axis
Pole (P)
Principal focus (F)
Center of curvature ©
Object
Image
Incident rays
Reflected rays

Diagram 7: Convex Mirror Ray Diagram

How to draw:

Draw a convex mirror (curved outward) as a vertical arc
Draw the principal axis as a horizontal line through the center
Mark Pole (P) and Principal Focus (F) behind the mirror
Draw an object (upward arrow) in front of mirror
Draw 2 key rays from top of object:
- Ray parallel to principal axis → reflects as if coming from F behind mirror
- Ray toward F behind mirror → reflects parallel to principal axis
Extend reflected rays backward with dashed lines
Where dashed lines meet behind mirror, draw the image (upright, diminished, virtual)

Labels needed:

Principal axis
Pole (P)
Principal focus (F) behind mirror
Object
Image (dashed, behind mirror)
Incident rays (solid)
Reflected rays (solid)
Extended rays (dashed behind mirror)

Diagram 8: Converging Lens Ray Diagram

How to draw:

Draw a vertical line with convex bulges on both sides (lens symbol)
Draw the principal axis horizontally through the center
Mark the Optical Center (O) and Principal Focus (F) on both sides
Draw an object (upward arrow) beyond F on the left
Draw 3 key rays from top of object:
- Ray parallel to principal axis → refracts through F on right
- Ray through F on left → emerges parallel to principal axis
- Ray through optical center → passes straight through
Where rays converge on right side, draw the image (inverted, real)

Labels needed:

Converging lens
Principal axis
Optical center (O)
Principal focus (F) on both sides
Object
Image (inverted)
Ray paths

Diagram 9: Diverging Lens Ray Diagram

How to draw:

Draw a vertical line with concave indents on both sides (lens symbol)
Draw the principal axis horizontally through the center
Mark the Optical Center (O) and Principal Focus (F) on both sides
Draw an object (upward arrow) on the left
Draw 2 key rays from top of object:
- Ray parallel to principal axis → diverges as if coming from F on left
- Ray toward F on right → emerges parallel to principal axis
Extend diverging rays backward with dashed lines on the left
Where dashed lines meet, draw the image (upright, diminished, virtual)

Labels needed:

Diverging lens
Principal axis
Optical center (O)
Principal focus (F) on both sides
Object
Image (dashed, upright, smaller)
Ray paths (solid through lens, dashed for extensions)

Worked Examples

Example 1: Calculating Angle of Reflection

Question: A light ray strikes a plane mirror at an angle of 35° to the mirror surface. Calculate the angle of reflection.

Solution: Step 1: Identify what angle is given

Given: angle to the mirror surface = 35°
Remember: angles in reflection are measured from the NORMAL, not the surface

Step 2: Calculate the angle of incidence from the normal

Normal is perpendicular to the surface (90° to surface)
Angle of incidence (i) = 90° - 35° = 55°

Step 3: Apply the law of reflection

Law of reflection: angle of incidence = angle of reflection
Therefore: angle of reflection ® = 55°

Answer: The angle of reflection is 55° (measured from the normal).

Note: If the question asks for the angle between the reflected ray and the mirror surface, it would be 90° - 55° = 35°.

Example 2: Calculating Refractive Index

Question: A ray of light enters a glass block from air. The angle of incidence is 60° and the angle of refraction is 35°. Calculate the refractive index of the glass.

Solution: Step 1: Write down what is given

Medium 1: air (n₁ = 1.0)
Angle of incidence: i = 60°
Angle of refraction: r = 35°
Medium 2: glass (n₂ = ?)

Step 2: Choose the correct formula

Since light enters from air: n = sin i / sin r

Step 3: Substitute values

n = sin 60° / sin 35°
n = 0.866 / 0.574
n = 1.51

Answer: The refractive index of the glass is 1.51 (or 1.5 to 2 significant figures).

Check: This answer makes sense because:

Glass typically has n between 1.5 and 1.6
Light bends toward the normal (60° → 35°), confirming glass is denser than air

Example 3: Calculating Critical Angle

Question: The refractive index of water is 1.33. Calculate the critical angle for light traveling from water to air.

Solution: Step 1: Write down what is given

n₁ (water) = 1.33
n₂ (air) = 1.0
Critical angle © = ?

Step 2: Identify the correct formula

Formula for critical angle: sin c = n₂/n₁
Note: This only works when light goes from denser to less dense medium

Step 3: Substitute values

sin c = 1.0 / 1.33
sin c = 0.752

Step 4: Find the angle

c = sin⁻¹(0.752)
c = 48.8°

Answer: The critical angle is 48.8° or approximately 49°.

Interpretation: When light travels from water to air at any angle greater than 49° to the normal, total internal reflection occurs and no light escapes into the air.

Common Mistakes to Avoid

Reflection Errors

❌ Measuring angles from the surface instead of the normal - ALWAYS measure from the normal (perpendicular line)
❌ Forgetting to draw the normal as a dashed line perpendicular to the surface
❌ Drawing the normal at any random angle instead of exactly 90° to the surface
❌ Making the angle of incidence and angle of reflection different sizes - they must be equal
❌ Forgetting arrows on ray diagrams to show direction of light travel

Refraction Errors

❌ Bending light the wrong way: Remember - toward normal when entering denser medium, away from normal when entering less dense medium
❌ Confusing which medium is denser: glass/water are denser than air
❌ Using the wrong formula: n = sin i / sin r only works when light enters from air (n₁ = 1)
❌ Forgetting to use Snell’s law correctly: n₁ sin i = n₂ sin r (not just n sin i = sin r)
❌ Not checking calculator is in DEGREE mode when calculating angles

Total Internal Reflection Errors

❌ Thinking TIR can occur when light goes from less dense to denser medium - NO! Only denser to less dense
❌ Drawing a refracted ray when angle > critical angle - there should be NO refracted ray, only reflection
❌ Confusing critical angle with angle of refraction of 90°: critical angle is the angle of incidence (in the denser medium)
❌ Stating only one condition for TIR - you need BOTH conditions (denser to less dense AND angle > critical angle)

Mirror and Lens Errors

❌ Saying plane mirror images are “behind the mirror” without specifying they are VIRTUAL
❌ Forgetting that plane mirror images are laterally inverted (not upside down)
❌ Stating image distance without comparing to object distance (they are equal for plane mirrors)
❌ Confusing concave and convex: concave curves inward, convex curves outward
❌ Saying a concave mirror always produces real images - it can produce virtual images too when object is between F and mirror
❌ Forgetting that convex mirrors and diverging lenses ALWAYS produce virtual, upright, diminished images

Ray Diagram Errors

❌ Not using a ruler for straight lines - ray diagrams must be neat and accurate
❌ Drawing rays that don’t obey the laws (e.g., ray parallel to principal axis not passing through focus)
❌ Not extending rays with dashed lines behind mirrors/lenses to locate virtual images
❌ Forgetting to label the image as “real” or “virtual”
❌ Drawing too few rays - you need at least 2 rays to locate an image position accurately

Terminology Errors

❌ Using “bouncing” instead of “reflection” - use proper scientific terms
❌ Saying light “bounces off the normal” - light reflects off the SURFACE, angles measured from normal
❌ Confusing “focal length” with “focal point” - length is a distance, point is a location
❌ Writing “light bends because it slows down” without explaining the medium change - be specific about cause

Exam Tips

Keywords and Phrases to Use

Always write “measured from the normal” when stating angles in reflection/refraction
Use “law of reflection” explicitly when stating i = r
For refraction, write “light bends toward/away from the normal as it enters a denser/less dense medium”
State conditions clearly: “TIR occurs when: (1) light travels from denser to less dense medium AND (2) angle of incidence > critical angle”
Describe images with all characteristics: “virtual, upright, same size, laterally inverted, same distance behind mirror” (for plane mirrors)
Use the term “laterally inverted” not just “reversed”

Drawing Ray Diagrams (Method Marks)

Use a ruler for all straight lines - you can lose marks for untidy diagrams
Draw normal lines as dashed - solid lines are only for actual light rays and boundaries
Add arrowheads on rays to show direction of light
Label all key points: P, F, C for mirrors; O, F for lenses
Use at least 2 rays to locate image position accurately
Extend virtual rays with dashed lines behind mirrors/lenses
When asked to “draw” or “construct” - accuracy matters; when asked to “sketch” - just show the pattern

Calculations (Maximum Marks)

Write the formula first before substituting - shows you know the method
Show substitution clearly: e.g., n = sin 60° / sin 35° = 0.866/0.574
State the formula for critical angle carefully: sin c = n₂/n₁ or sin c = 1/n (when n₂ = air)
Include units where appropriate (degrees for angles)
Give answers to appropriate significant figures (usually 2 or 3 s.f.)
Check your answer makes sense: refractive index should be > 1, critical angle should be < 90°

Explanation Questions

Use “because” to link cause and effect: “Light bends toward the normal because it enters a denser medium and slows down”
State the physics principle first: “According to the law of reflection, angle of incidence equals angle of reflection”
For TIR applications, explain: “Optical fibers use TIR to keep light trapped inside, allowing signals to travel long distances without escaping”
Comparison questions: Use “whereas” or “while” - “A concave mirror converges light, whereas a convex mirror diverges light”

Image Description Questions

For plane mirrors, state ALL characteristics:

Virtual (cannot be projected on screen)
Upright (same orientation as object)
Same size as object
Laterally inverted (left-right reversed)
Same distance behind mirror as object is in front

For curved mirrors/lenses, state:

Real or virtual
Upright or inverted
Magnified, same size, or diminished
Position relative to lens/mirror

Common Command Words

“State”: Give the law/rule directly (no explanation needed)
“Explain”: Give reason using physics principles
“Draw”: Accurate diagram with ruler, labeled
“Sketch”: Show shape/pattern (less accuracy needed)
“Calculate”: Show formula, substitution, answer with unit
“Describe”: Give characteristics systematically

Time-Saving Tips

Learn the standard ray paths for mirrors and lenses - don’t work them out each time
For calculations, write the formula immediately - don’t waste time thinking about the substitution first
Practice drawing quick accurate normals with a set square or protractor
Memorize critical values: critical angle for glass ≈ 42°, water ≈ 49°; refractive index glass ≈ 1.5, water ≈ 1.33

Quick Summary

Essential checklist for revision:

✓ Laws of reflection: (1) Incident ray, reflected ray, and normal lie in same plane; (2) Angle of incidence equals angle of reflection (i = r), measured from the normal

✓ Refraction basics: Light bends toward normal entering denser medium (slows down), away from normal entering less dense medium (speeds up)

✓ Snell’s Law: n₁ sin i = n₂ sin r; for air to medium: n = sin i / sin r

✓ Total Internal Reflection conditions: (1) Light travels denser → less dense medium; (2) Angle of incidence > critical angle; formula: sin c = n₂/n₁

✓ Plane mirror image: Virtual, upright, same size, laterally inverted, equal distance behind mirror as object is in front

✓ Concave mirror: Converging; can produce real (inverted) or virtual (upright, magnified) images; used in makeup mirrors, torches

✓ Convex mirror: Diverging; always produces virtual, upright, diminished images; wider field of view; used in vehicle mirrors

✓ Converging lens: Thicker at center; converges parallel rays to real focus; can form real or virtual images depending on object position

✓ Diverging lens: Thinner at center; diverges parallel rays; always produces virtual, upright, diminished images

✓ Key terms: Normal (perpendicular to surface), principal axis, focal length (f = r/2 for mirrors), real vs virtual images, refractive index

✓ Ray diagrams: Use ruler, draw normal as dashed line, add arrows, label all key points (P, F, C, O), use at least 2 rays to locate images

✓ Calculations: Write formula first, show substitution, check calculator in degree mode, give appropriate significant figures, include units for angles (°)

Remember: Practice drawing ray diagrams regularly - accuracy and neatness earn marks in exams!