Reflection of Light - Mirror Systems
The Movie Hook 🎬
Remember the mirror scene in Inception where Ariadne creates infinite reflections? Or how John Wick uses mirror angles to spot enemies? These aren’t just cool effects - they’re perfect demonstrations of reflection laws that JEE loves to test!
The Big Picture
Reflection is light’s “bounce-back” behavior when it hits a surface. Understanding this is crucial for:
- Curved mirrors (concave/convex)
- Optical instruments (telescopes, headlights)
- Ray diagrams (the heart of JEE problems)
Connection Alert: This links directly to Wave Optics and Refraction.
Core Concepts
1. Laws of Reflection
First Law: The incident ray, reflected ray, and normal all lie in the same plane.
Second Law: Angle of incidence = Angle of reflection
$$\boxed{i = r}$$Memory Trick: “I R equal” (i = r) - imagine yourself saying “I are equal” in broken English!
2. Plane Mirrors
Properties:
- Image is virtual, erect, and same size
- Image distance = Object distance: $$\boxed{v = -u}$$
- Lateral inversion (left becomes right)
Key Formula for Rotation: When mirror rotates by angle θ, reflected ray rotates by 2θ
$$\boxed{\text{Reflected ray deviation} = 2\theta}$$JEE Trick: For two plane mirrors at angle θ:
$$\boxed{n = \frac{360°}{\theta} - 1}$$(number of images)
If 360°/θ is not an integer, take the floor value.
3. Spherical Mirrors
Sign Convention (NEW CARTESIAN - CRUCIAL!)
Most Common Mistake: Forgetting sign conventions!
- Distances measured from pole P
- Towards object (left): Negative
- Away from object (right): Positive
- Above principal axis: Positive height
- Below principal axis: Negative height
Mirror Formula
$$\boxed{\frac{1}{v} + \frac{1}{u} = \frac{1}{f}}$$Where:
- u = object distance (usually negative)
- v = image distance
- f = focal length
- Concave: f is negative (f = -R/2)
- Convex: f is positive (f = +R/2)
Magnification Formula
Linear Magnification:
$$\boxed{m = -\frac{v}{u} = \frac{h_i}{h_o}}$$Negative m → Inverted image Positive m → Erect image
Memory Trick: “Minus V Under” (m = -v/u)
4. Concave vs Convex Mirrors
| Property | Concave (Converging) | Convex (Diverging) |
|---|---|---|
| Focal length | Negative | Positive |
| Image for real object | Can be real or virtual | Always virtual |
| Magnification | Can be >1, =1, or <1 | Always <1 |
| Uses | Shaving mirrors, telescopes | Rear-view mirrors, security |
5. Ray Diagrams - The JEE Shortcut
For Concave Mirrors: Three principal rays:
- Parallel to axis → Passes through F after reflection
- Through F → Parallel to axis after reflection
- Through C → Retraces path (perpendicular to mirror)
Quick Position Rules:
| Object Position | Image Position | Nature | Size |
|---|---|---|---|
| At infinity | At F | Real, inverted | Point-sized |
| Beyond C | Between F and C | Real, inverted | Diminished |
| At C | At C | Real, inverted | Same size |
| Between C and F | Beyond C | Real, inverted | Magnified |
| Between F and P | Behind mirror | Virtual, erect | Magnified |
| At F | At infinity | Real, inverted | Highly magnified |
Memory Acronym: “Infinity Brings Focus Closer Between F-C Creates Bigger Copies” (weird but works!)
The Formula Cheat Sheet
MIRROR ESSENTIALS:
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1. Mirror formula: 1/v + 1/u = 1/f
2. Magnification: m = -v/u = h_i/h_o
3. Focal length: f = R/2
4. Rotation effect: Deviation = 2θ
5. Multiple images: n = 360°/θ - 1
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Common Traps & Mistakes
Trap #1: Sign Convention Chaos
❌ Wrong: Taking all values as positive ✅ Right: Object distance u is ALWAYS negative for real objects
Trap #2: Confusing R and f
❌ Wrong: Using R instead of f in mirror formula ✅ Right: f = R/2, use f in the formula
Trap #3: Magnification Interpretation
❌ Wrong: m = 2 means image is twice as far ✅ Right: m = 2 means image HEIGHT is twice the object height
Practice Problems
Level 1: JEE Main Warmup
Problem 1.1: A concave mirror has a focal length of 20 cm. An object is placed 30 cm in front of it. Find the image position and magnification.
Solution
Given: f = -20 cm, u = -30 cm
Using mirror formula:
$$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$ $$\frac{1}{v} = \frac{1}{-20} - \frac{1}{-30} = -\frac{1}{20} + \frac{1}{30} = \frac{-3+2}{60} = -\frac{1}{60}$$ $$v = -60 \text{ cm}$$Magnification:
$$m = -\frac{v}{u} = -\frac{(-60)}{(-30)} = -2$$Answer: Image at 60 cm in front (real), magnified 2x, inverted
Problem 1.2: Two plane mirrors are inclined at 60°. How many images will be formed?
Solution
Answer: 5 images
Level 2: JEE Main/Advanced
Problem 2.1: A convex mirror has a radius of curvature 40 cm. An object is placed 20 cm from the mirror. Find (a) image position (b) magnification (c) nature of image.
Solution
Given: R = +40 cm (convex), so f = R/2 = +20 cm u = -20 cm (object is in front)
Mirror formula:
$$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$ $$\frac{1}{v} = \frac{1}{20} - \frac{1}{-20} = \frac{1}{20} + \frac{1}{20} = \frac{2}{20} = \frac{1}{10}$$ $$v = +10 \text{ cm}$$Magnification:
$$m = -\frac{v}{u} = -\frac{10}{-20} = +0.5$$Answers:
- (a) Image at 10 cm behind mirror
- (b) m = 0.5 (half size)
- (c) Virtual, erect, diminished (positive v and positive m confirm this)
Problem 2.2: A plane mirror is rotating at 5 rev/min. What is the angular velocity of the reflected light beam?
Solution
Mirror rotates: ω = 5 rev/min Reflected ray rotates at: 2ω = 10 rev/min
Converting to rad/s:
$$\omega_{\text{reflected}} = 10 \times \frac{2\pi}{60} = \frac{\pi}{3} \text{ rad/s}$$Answer: π/3 rad/s or 10 rpm
Level 3: JEE Advanced
Problem 3.1: A small object is placed at the center of curvature of a concave mirror. The mirror starts moving towards the object with speed v. At what speed will the image move and in which direction?
Solution
When object is at C, image is also at C with m = -1.
Using mirror formula and differentiating:
$$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$At C: u = -2f, v = -2f
Differentiating w.r.t. time:
$$-\frac{1}{v^2}\frac{dv}{dt} - \frac{1}{u^2}\frac{du}{dt} = 0$$Since mirror moves with speed v towards object, object distance decreases:
$$\frac{du}{dt} = -v_{\text{mirror}} = -v$$ $$\frac{dv}{dt} = -\frac{v^2}{u^2}\frac{du}{dt} = -\frac{(-2f)^2}{(-2f)^2}(-v) = -v$$But we need speed of image relative to ground. Since mirror moves with v and image position changes at rate -v relative to mirror:
Image speed relative to ground = v (mirror speed) + v (relative to mirror) = 2v towards mirror
Answer: Image moves at 2v towards the mirror
Problem 3.2: A point source is placed at distance 2f from a concave mirror of focal length f. A glass slab of thickness t and refractive index μ is placed between source and mirror perpendicular to principal axis. Find the position of final image.
Solution
Due to glass slab, apparent shift occurs:
$$\text{Shift} = t\left(1 - \frac{1}{\mu}\right)$$Effective object distance from mirror:
$$u_{\text{eff}} = -2f + t\left(1 - \frac{1}{\mu}\right)$$Using mirror formula:
$$\frac{1}{v} + \frac{1}{u_{\text{eff}}} = \frac{1}{f}$$ $$\frac{1}{v} = \frac{1}{f} - \frac{1}{u_{\text{eff}}}$$For exact position, substitute the shift value.
Concept: Slab causes shift = t(1 - 1/μ), making object appear closer by this amount.
Answer:
$$v = \frac{f \cdot u_{\text{eff}}}{u_{\text{eff}} - f}$$where
$$u_{\text{eff}} = -2f + t(1-1/\mu)$$Quick Revision Cards
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║ REFLECTION QUICK FACTS ║
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🎯 Laws: i = r, same plane
🎯 Plane mirror: v = -u, m = +1
🎯 Mirror formula: 1/v + 1/u = 1/f
🎯 m = -v/u = h_i/h_o
🎯 f = R/2 (concave: -, convex: +)
🎯 Rotation: beam rotates 2θ
🎯 Images: n = 360°/θ - 1
Cross-Topic Connections
- Refraction: Combined mirror-lens systems
- Thin Lens: Similar formula approach
- Optical Instruments: Telescopes use mirrors
- Wave Optics: Phase change on reflection
Exam Strategy
Time Allocation:
- Ray diagram: 2 min
- Formula application: 3 min
- Numerical calculation: 2 min
Common JEE Patterns:
- Object moving with velocity → Use differentiation
- Multiple reflections → Track each reflection systematically
- Field of view problems → Use geometry + reflection laws
- Combined mirror systems → Apply formula sequentially
Final Tips
- Always draw a ray diagram first - even roughly
- Check signs before substituting in formulas
- Verify if answer makes physical sense (real/virtual, magnified/diminished)
- For numerical problems, write down sign convention at the start
Remember: Reflection is the foundation for all optics. Master this, and curved mirrors become trivial!
Next up: Refraction - where light bends instead of bounces!