Light: Reflection & Refraction — Mirror & Lens Formulas With Examples

Light: Reflection & Refraction — Mirror & Lens Formulas Made Easy

Light behaves in predictable ways. Understanding reflection (bouncing off mirrors) and refraction (bending through lenses) is crucial for CBSE, ICSE, and IB physics, and explains how mirrors and glasses work.

In this guide, we'll master the laws of reflection and refraction, formula application, and sign conventions that often confuse students.

Part 1: Reflection of Light

Law of Reflection

The law of reflection states: The angle of incidence equals the angle of reflection, and both lie in the same plane as the normal.

Key terms:

• Incident ray: Light approaching the mirror
• Reflected ray: Light bouncing off the mirror
• Normal: Perpendicular line to the mirror surface
• Angle of incidence (i): Angle between incident ray and normal
• Angle of reflection (r): Angle between reflected ray and normal

The Law: i = r

Types of Mirrors

1. Plane Mirrors (Flat)

Image characteristics:

Virtual (appears behind mirror)

Erect (upright)

Same size as object

Same distance behind mirror as object is in front

Formula: Not needed for plane mirrors (simple geometry) Real-life use: Bathroom mirrors, wardrobe mirrors

2. Concave Mirrors (Curved inward)

Converging mirror – Reflects light toward a single point (focus). Key points:

Focal point (F): Where reflected rays meet

Center of curvature (C): Center of the sphere (R = 2F)

Principal axis: Line through C and F

Mirror Formula: CODEBLOCK0 Magnification: CODEBLOCK1 Sign Convention (Most Important!):

Distances measured from mirror

Toward mirror (real): Positive

Away from mirror (virtual): Negative

Upright: Positive height

Inverted: Negative height

3. Convex Mirrors (Curved outward)

Diverging mirror – Reflects light away from a point. Key characteristics:

Always virtual image

Always erect and diminished

Focal point is behind mirror (negative)

Same formulas apply with sign convention:

f is negative (diverging)

v is always negative (virtual image behind mirror)

Real-life use: Rear-view mirrors in vehicles, security mirrors

Sign Convention for Mirrors (Detailed)

CODEBLOCK2 Memory tip: In front of mirror = positive (real), Behind mirror = negative (virtual)

Mirror Formula Examples

Example 1: Concave Mirror

Object 30 cm in front of concave mirror with f = 10 cm. Find image position and nature.

Solution: CODEBLOCK3 Example 2: Convex Mirror

Object 15 cm in front of convex mirror with f = -10 cm. Find image.

Solution: CODEBLOCK4

Part 2: Refraction of Light

Law of Refraction (Snell's Law)

Refraction is the bending of light when passing from one medium to another.

Snell's Law: CODEBLOCK5 Key terms:

Refractive index (n): How much a medium slows down light

Air: n ≈ 1

Water: n ≈ 1.33

Glass: n ≈ 1.5

Diamond: n ≈ 2.4 (extremely high, why it sparkles)

Understanding Refraction

Light slowing down (entering denser medium): Bends toward normal

Light speeding up (leaving denser medium): Bends away from normal

Analogy: Like a car wheel going from pavement to sand at an angle—the wheel in sand slows first, turning the car.

Critical Angle and Total Internal Reflection

When light travels from a denser to less dense medium at a steep angle, it may undergo total internal reflection (bounces back completely).

Critical angle (C): CODEBLOCK6

If angle of incidence > critical angle, total internal reflection occurs.

Examples:

Diamond sparkles because light undergoes total internal reflection (high n)

Fiber optic cables use total internal reflection

Mirages in deserts (light from sky undergoes total internal reflection in hot air layer)

Part 3: Lenses

Types of Lenses

1. Convex Lens (Converging)

Thicker in the middle, brings light rays together.

Focal length (f): Positive Focal point: Where parallel rays meet Uses: Magnifying glass, camera lens, microscope objective

2. Concave Lens (Diverging)

Thinner in the middle, spreads light rays apart.

Focal length (f): Negative Virtual focal point: Where diverging rays appear to come from Uses: Spectacles for myopia (short-sightedness)

Lens Formula

The lens formula is identical to mirror formula:

CODEBLOCK7 Sign Convention for Lenses:

Object distance (u): + if object is in front (real)

Image distance (v): + if image is on opposite side (real), - if on same side (virtual)

Focal length (f): + for convex (converging), - for concave (diverging)

Lens Formula Example

Convex lens with f = 15 cm, object 45 cm away: CODEBLOCK8

Power of a Lens

Power (P): Ability of lens to converge or diverge light. CODEBLOCK9 Example: A +2 D lens has f = 0.5 m = 50 cm (convex, converging) Uses: Spectacle prescriptions are written in diopters.

Ray Diagrams: Visual Method

For mirrors and lenses, ray diagrams show image formation graphically.

Three Principal Rays for Convex Lens

1. Ray parallel to axis: Passes through focus F
2. Ray through focus F: Becomes parallel to axis
3. Ray through center O: Passes straight (undeviated)

Image is where rays meet (or appear to come from).

Three Principal Rays for Concave Mirror

Ray parallel to axis: Passes through focus F

Ray toward focus F: Reflects parallel to axis

Ray toward center C: Reflects back along same path

Quick Recap: Formulas and Signs

Real-World Applications

Mirrors

Concave: Shaving mirrors, satellite dishes, solar furnaces

Convex: Vehicle rear-view mirrors, security mirrors

Lenses

Convex: Cameras, projectors, magnifying glass, microscope objectives

Concave: Correction for myopia (short-sightedness)

Combination: Telescopes, binoculars, compound microscopes

Refraction Applications

Rainbow: Refraction and dispersion of sunlight in water droplets

Mirages: Total internal reflection in hot air layers

Fiber optics: Total internal reflection for data transmission

Magnifying glass: Convex lens uses refraction

Try This: Practice Problems

Plane mirror: Object 5 cm from mirror. Where is image? What type?

Concave mirror: f = 20 cm, object 30 cm away. Find image distance and magnification.

Convex lens: f = 10 cm, object 20 cm away. Find image distance and magnification.

Refraction: Light hits water surface at 45°. If nair = 1, nwater = 1.33, find refraction angle.

Lens power: A lens has f = 25 cm. Calculate its power in diopters.

Exam Questions: CBSE/ICSE Pattern

Q1: State the law of reflection.

A: Angle of incidence = Angle of reflection, both measured from normal, in same plane.

Q2: A mirror forms a real, inverted, enlarged image. What type of mirror is it?

A: Concave mirror with object between F and C.

Q3: Derive the mirror formula: 1/f = 1/u + 1/v

A: [Using similar triangles and geometry of ray diagrams]

Q4: What is refractive index? Name a material with n > 1.33 (water).

A: Refractive index is the ratio of speed of light in vacuum to speed in the medium. Glass (n ≈ 1.5), diamond (n ≈ 2.4).

Q5: A convex lens of power +2D is used. Find its focal length.

A: P = 1/f → 2 = 1/f → f = 0.5 m = 50 cm

FAQ: Light, Reflection and Refraction

Q: Why do objects underwater appear closer than they actually are?

A: Light refracts when moving from water to air. The apparent position is different from actual position due to refraction.

Q: Why does a diamond sparkle more than glass?

A: Diamond's higher refractive index (2.4 vs 1.5) causes more refraction and total internal reflection, creating more sparkle.

Q: Can a concave lens form a real image?

A: No, concave (diverging) lenses always form virtual, erect, diminished images. Real images require converging lenses (under normal conditions).

Q: What's the difference between a real and virtual image?

A: Real images can be projected on a screen; virtual images cannot. Real images are inverted; virtual images are erect.

Q: Why do swimming pools look shallower than they actually are?

A: Due to refraction of light at the water surface. Light bends as it exits water, making objects underwater appear closer to the surface.

Next Steps

Now that you understand light, explore related topics:

Electricity and Circuits – How light is produced in light bulbs

Periodic Table – Elements in optical materials (silicon in fiber optics)

Photosynthesis – How plants capture light energy

Practice with The Practise Ground physics quizzes for more ray diagram practice!

Light is one of the most fascinating topics in physics. Understanding reflection and refraction opens the door to understanding optical instruments, mirages, rainbows, and the behavior of light itself. Master these concepts, and you'll see the world with new clarity. Good luck with your exams!