Physics Optics
Key Concepts & Formulas
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Reflection Law | θᵢ = θᵣ (Angle of incidence = Angle of reflection) |
| 2 | Refractive Index | n = c/v = sin i/sin r (Speed ratio & Snell’s law) |
| 3 | Mirror Formula | 1/f = 1/v + 1/u (f = focal length, u = object, v = image) |
| 4 | Lens Formula | 1/f = 1/v - 1/u (Sign convention: real = positive) |
| 5 | Power of Lens | P = 1/f (in diopters, f in meters) |
| 6 | Total Internal Reflection | Occurs when n₁ > n₂ and θ > θc = sin⁻¹(n₂/n₁) |
| 7 | Magnification | m = h’/h = -v/u (Negative = inverted image) |
10 Practice MCQs
Q1. A train headlight produces parallel beam of light. Which mirror is used? A) Concave B) Convex C) Plane D) Cylindrical
Answer: A) Concave
Solution: When object is placed at focus (f) of concave mirror, reflected rays become parallel. Train headlights use this principle.
Shortcut: “Headlights need parallel beams → Concave mirror at focus”
Concept: Physics Optics - Mirror applications
Q2. Speed of light in glass (n=1.5) is ×10⁸ m/s: A) 3.0 B) 2.0 C) 1.5 D) 4.5
Answer: B) 2.0
Solution: v = c/n = (3×10⁸)/1.5 = 2×10⁸ m/s
Shortcut: Speed decreases in denser medium → Divide by n
Concept: Physics Optics - Refractive index
Q3. A platform mirror forms erect image 2m behind mirror. Object distance is: A) 1m B) 2m C) 4m D) 0.5m
Answer: B) 2m
Solution: Plane mirror: image distance = object distance
Shortcut: Plane mirror → Image distance = Object distance
Concept: Physics Optics - Plane mirror properties
Q4. Railway signal lens has power +5D. Its focal length is: A) 5cm B) 20cm C) 50cm D) 2cm
Answer: B) 20cm
Solution: f = 1/P = 1/5 = 0.2m = 20cm
Shortcut: f(cm) = 100/P(D)
Concept: Physics Optics - Lens power
Q5. Critical angle for glass-water interface (n_glass=1.5, n_water=1.33): A) 62.5° B) 48.6° C) 41.8° D) 30.2°
Answer: A) 62.5°
Solution: θc = sin⁻¹(n₂/n₁) = sin⁻¹(1.33/1.5) = sin⁻¹(0.887) = 62.5°
Shortcut: θc = sin⁻¹(rarer/denser)
Concept: Physics Optics - Total internal reflection
Q6. A 6m tall electric pole creates 3m shadow. If station building's shadow is 24m, its height is: A) 12m B) 48m C) 36m D) 24m
Answer: B) 48m
Solution: Using similar triangles: h₁/h₂ = s₁/s₂ → 6/h = 3/24 → h = 48m
Shortcut: Height ∝ Shadow length (same time)
Concept: Physics Optics - Shadow formation & similar triangles
Q7. Convex mirror (f=20cm) shows image at 10cm when object is at: A) 30cm B) 20cm C) 15cm D) 10cm
Answer: B) 20cm
Solution: Using 1/f = 1/v + 1/u with f=+20cm, v=+10cm → 1/20 = 1/10 + 1/u → u = -20cm
Shortcut: Convex mirror: virtual image always closer than object
Concept: Physics Optics - Mirror formula
Q8. Two platform lights 60m apart appear merged when viewed through telescope with angular resolution 0.01°. Maximum viewing distance is: A) 34.4km B) 3.44km C) 344m D) 344km
Answer: A) 34.4km
Solution: d = s/θ = 60/(0.01×π/180) = 60×180×7/22 = 34,363m ≈ 34.4km
Shortcut: d(km) ≈ s(m)/θ(degrees)×57.3
Concept: Physics Optics - Angular resolution
Q9. A train passes under 440Hz whistle. If heard as 400Hz, train speed is (sound speed=340m/s): A) 34m/s B) 30.9m/s C) 27.6m/s D) 25m/s
Answer: B) 30.9m/s
Solution: f’ = f(v-v₀)/v → 400 = 440(340-v)/340 → v = 340(1-400/440) = 30.9m/s
Shortcut: Δf/f ≈ v_train/v_sound (for v«v_sound)
Concept: Physics Optics - Doppler effect
Q10. Railway track appears shimmering on hot day due to: A) Diffraction B) Total reflection C) Refraction D) Interference
Answer: C) Refraction
Solution: Hot air layers have varying density → varying refractive index → light bends differently
Shortcut: “Shimmer = Air layers = Refraction”
Concept: Physics Optics - Atmospheric refraction
5 Previous Year Questions
PYQ 1. The power of a lens is -2.5D. The lens is: [RRB NTPC 2021 CBT-1]
Answer: B) Concave lens of focal length -40cm
Solution: P = 1/f → f = 1/(-2.5) = -0.4m = -40cm. Negative focal length = concave lens
Exam Tip: Negative power always indicates concave/diverging lens
PYQ 2. A concave mirror forms real image twice size of object. If object is at 15cm, focal length is: [RRB Group D 2022]
Answer: C) 10cm
Solution: m = -2 (real = negative), v = -2u = -30cm. Using 1/f = 1/v + 1/u = 1/(-30) + 1/(-15) = -3/30 → f = -10cm
Exam Tip: Remember sign convention: real images have negative magnification
PYQ 3. Critical angle for diamond (n=2.42) is approximately: [RRB ALP 2018]
Answer: B) 24.4°
Solution: θc = sin⁻¹(1/2.42) = sin⁻¹(0.413) = 24.4°
Exam Tip: High refractive index → Low critical angle → More brilliant gems
PYQ 4. A locomotive headlight uses mirror of focal length 10cm. Where should bulb be placed for parallel beam? [RRB JE 2019]
Answer: A) At focus (10cm)
Solution: For parallel reflected rays, place object at focus of concave mirror
Exam Tip: Applications: Headlights, searchlights, torch → Object at focus
PYQ 5. The refractive index of glass with respect to water is: [RPF SI 2019]
Answer: C) 1.5/1.33 = 1.13
Solution: n_glass/water = n_glass/n_water = 1.5/1.33 = 1.13
Exam Tip: Relative refractive index = n₁/n₂
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| Finding image nature | “REAL VS” - Real images: Virtual when object inside focus for mirrors, Virtual when object inside focus for lenses | Convex mirror: always virtual. Concave: real if u>f, virtual if u<f |
| Power to focal length | f(cm) = 100/P(D) | P = +4D → f = 25cm |
| Critical angle memory | “Higher n → Lower θc” | Diamond (n=2.4) → θc≈24°, Water (n=1.33) → θc≈49° |
| Magnification sign | “REAL negative, VIRTUAL positive” | m = -2 → real, inverted, 2× size |
| Mirror/Lens applications | “CCTV - C=Concave, V=Vehicle headlights, T=Telescope, V=Venus” | Convex: rear view, Concave: shaving, dentist |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Sign convention errors | Confusing real/virtual directions | Always use: Light → +ve, Real images → -ve magnification |
| Forgetting n = c/v | Using v = c×n instead of c/n | Speed decreases in denser medium → v = c/n |
| Angular resolution units | Using degrees directly in formulas | Convert to radians: θ(rad) = θ(°)×π/180 |
| Mirror vs lens formula | Using same formula for both | Mirror: 1/f = 1/v + 1/u, Lens: 1/f = 1/v - 1/u |
| Critical angle condition | Forgetting n₁>n₂ requirement | TIR only when going denser→rarer at θ>θc |
Quick Revision Flashcards
| Front (Question/Term) | Back (Answer) |
|---|---|
| Snell’s Law | n₁sinθ₁ = n₂sinθ₂ |
| Lens maker’s formula | 1/f = (n-1)(1/R₁ - 1/R₂) |
| Power unit | Diopter (D) = m⁻¹ |
| Total magnification | m_total = m₁ × m₂ × m₃… |
| Prism formula | δ = (n-1)A (for small A) |
| Rainbow formation | Dispersion + TIR in water droplets |
| Apparent depth | Real depth / n |
| Critical angle formula | θc = sin⁻¹(n₂/n₁) |
| Mirror magnification | m = -v/u = h’/h |
| Lens types by power | +ve = converging, -ve = diverging |
Topic Connections
Direct Links:
- Waves: Light as electromagnetic wave (c = fλ)
- Measurements: Vernier calipers measure lens thickness
- Heat: Infrared radiation from train engines
Combined Questions:
- Optics + Motion: Doppler effect with moving trains
- Optics + Energy: Solar panels using photovoltaic effect
- Optics + Electricity: LED signals in railway signaling
Foundation For:
- Modern Physics: Photoelectric effect, lasers
- Electronics: Optical fibers in communication
- Photography: Camera optics for surveillance
BETA
