Ray Optics and Optical Instruments

'Light may be a wave, but for MIRRORS and LENSES, the RAY model is all we need.'

1. Chapter Overview

Ray optics (geometrical optics) treats light as RAYS that travel in straight lines. Topics include: REFLECTION at spherical mirrors (mirror formula, magnification), REFRACTION (Snell's law, total internal reflection, critical angle), LENSES (lens maker's formula, lens formula, power of a lens, combination of lenses), the PRISM (angle of deviation, dispersion), and OPTICAL INSTRUMENTS (the microscope and telescope).

2. Reflection at Spherical Mirrors

Sign Convention (Cartesian)

• Distances measured from the POLE: TOWARDS incident light = NEGATIVE (real object). OPPOSITE = POSITIVE (virtual image).
• 'All distances are measured from the pole. Incident light direction is NEGATIVE.'

Mirror Formula

• 1/f = 1/v + 1/u — where u = object distance, v = image distance, f = focal length.
• Magnification: m = −v/u. m > 1 ⇒ enlarged, m < 1 ⇒ diminished.

Worked Example 1

Problem: An object is placed 15 cm from a concave mirror of focal length 10 cm. Find image position and magnification. Solution: u = −15 cm, f = −10 cm. 1/v = 1/f − 1/u = −1/10 + 1/15 = (−3+2)/30 = −1/30. v = −30 cm (REAL, in front of mirror). m = −v/u = −(−30)/(−15) = −2 (INVERTED, ENLARGED).

3. Refraction — Snell's Law

• n₁ sin θ₁ = n₂ sin θ₂ — the BEND of light when passing between media.
• Refractive index: n = c/v. 'Absolute refractive index = speed of light in vacuum / speed in medium.'

Total Internal Reflection (TIR)

• Condition: (1) Light goes from DENSER to RARER medium. (2) Angle of incidence > CRITICAL ANGLE.
• Critical angle: C = sin⁻¹(n₂/n₁).

Applications of TIR

• Optical fibres: 'Light is KEPT inside the fibre by repeated TIR — enabling high-speed internet communication.'
• Prism in binoculars: Totally reflecting prisms produce an ERECT image.
• Mirage: 'The shimmering on a hot road — TIR of light from the sky due to varying refractive index of hot air near the ground.'

4. Lenses

Lens Maker's Formula

• 1/f = (μ − 1)(1/R₁ − 1/R₂) — f depends on refractive index AND curvature of both surfaces.

Lens Formula

• 1/f = 1/v − 1/u (sign convention: u is always NEGATIVE for real object).

Power of a Lens

• P = 1/f (f in metres). Unit: Dioptre (D).
• Combination of lenses: P = P₁ + P₂ + ... (in contact). Equivalent focal length: 1/f = 1/f₁ + 1/f₂ + ...

5. Prism

Angle of Deviation

• δ = i + e − A (where A = prism angle, i = angle of incidence, e = angle of emergence).
• Minimum deviation (δ_m) : When i = e and ray passes SYMMETRICALLY through the prism.
• δ_m = 2i − A — and from Snell's law: μ = sin[(A+δ_m)/2] / sin(A/2).

Dispersion

• 'White light splits into its constituent colours when passing through a prism — because the refractive index depends on WAVELENGTH.'
• λ_violet < λ_red ⇒ n_violet > n_red ⇒ violet bends MORE.
• Rainbow: 'A natural dispersion of sunlight by water droplets in the atmosphere.'

6. Optical Instruments

Simple Microscope

• Angular magnification: M = 1 + D/f (where D = 25 cm = near point). Image at D.

Compound Microscope

• M = M₀ × M_E = (L/f₀) × (1 + D/f_E). 'Objective produces a real, inverted, enlarged image. Eyepiece magnifies it further.'
• f₀ < f_E. Tube length L = distance between second focal point of objective and first focal point of eyepiece.

Astronomical Telescope (Refracting)

• M = −f₀/f_E. 'Objective has LARGE focal length. Eyepiece has SMALL focal length.'
• Length: L = f₀ + f_E.

7. Common Mistakes

1. Sign convention confusion: CBSE uses the CARTESIAN sign convention. BE CONSISTENT. For mirrors: u, f for concave = NEGATIVE. For lenses: u = NEGATIVE always.
2. Magnification for mirrors: m = −v/u. For lenses: m = v/u. 'The negative in the mirror formula accounts for the sign convention difference.'
3. Total internal reflection: The light MUST go from denser to rarer medium. TIR does NOT occur when going from rarer to denser.
4. Minimum deviation: The formula μ = sin[(A+δ_m)/2]/sin(A/2) is ONLY valid at MINIMUM deviation.

8. CBSE Exam Focus

1. Mirror formula — numerical problems (u, v, f, m)
2. Refraction — Snell's law, refractive index
3. Total internal reflection — critical angle, conditions, applications
4. Lens formula and lens maker's formula — numerical problems
5. Prism — deviation, minimum deviation, dispersion
6. Optical instruments — simple microscope, compound microscope, telescope (magnifying power, construction)

9. Self-Test

Q1: A convex lens of focal length 20 cm forms a real image at 30 cm. Find object distance. A1: 1/v − 1/u = 1/f ⇒ 1/30 − 1/u = 1/20 ⇒ −1/u = 1/20 − 1/30 = (3−2)/60 = 1/60 ⇒ u = −60 cm.

Q2: Find the critical angle for a glass-air interface (μ_g = 1.5). A2: C = sin⁻¹(1/μ) = sin⁻¹(1/1.5) = sin⁻¹(0.667) ≈ 41.8°.

Q3: A prism of angle 60° has minimum deviation 40°. Find refractive index. A3: μ = sin[(A+δ_m)/2]/sin(A/2) = sin(50°)/sin(30°) = 0.766/0.5 = 1.532.

Q4: A compound microscope has f₀ = 1 cm, f_E = 2.5 cm, tube length = 20 cm. Find magnification. A4: M = (L/f₀)(1 + D/f_E) = (20/1)(1 + 25/2.5) = 20(1 + 10) = 220.

Q5: An object is placed 5 cm from a concave mirror of focal length 10 cm. Find image position, nature, and magnification. A5: u = −5 cm, f = −10 cm. 1/v = 1/f − 1/u = −1/10 + 1/5 = 1/10. v = +10 cm (BEHIND mirror — VIRTUAL). m = −v/u = −10/(−5) = +2 (ERECT, ENLARGED).

10. Conclusion

Ray optics is the GEOMETRY of light:

• REFLECTION: 'Mirrors — angles of incidence and reflection are EQUAL. Everything else follows from geometry.'
• REFRACTION: 'Light BENDS when changing speed — Snell's law tells you by how much.'
• INSTRUMENTS: 'Microscopes make the small BIG. Telescopes make the FAR CLOSE. Both are clever arrangements of lenses.'
• TIR: 'Light trapped inside glass — the principle behind optical fibres and the internet.'

'Ray optics may be a SIMPLIFICATION of the wave nature of light — but it is an incredibly USEFUL one, enabling everything from eyeglasses to space telescopes.'