Class 12 Physics Notes Chapter 1 (Ray Optics and Optical Instruments) – Physics Part-II Book

Alright class, let's begin our focused revision of Chapter 9: Ray Optics and Optical Instruments from your NCERT Physics Part-II book. This chapter is crucial not just for your board exams but also forms a significant part of the syllabus for various government competitive exams. We'll break it down systematically, focusing on the core concepts and formulas you need to master.

Ray Optics and Optical Instruments: Key Concepts for Exam Preparation

1. Introduction to Ray Optics:

• Light travels in straight lines (rectilinear propagation) in a uniform medium. This path is called a ray. A bundle of rays is a beam.
• Ray optics (or geometrical optics) deals with image formation using rays, ignoring the wave nature of light (valid when obstacle/aperture size >> wavelength of light).

2. Reflection of Light:

• Laws of Reflection:
  • (i) The angle of incidence (∠i) equals the angle of reflection (∠r). (∠i = ∠r)
  • (ii) The incident ray, the reflected ray, and the normal to the reflecting surface at the point of incidence all lie in the same plane.
• Plane Mirror:
  • Forms a virtual, erect image.
  • Image is laterally inverted.
  • Image size is equal to object size (Magnification, m = +1).
  • Image distance is equal to object distance (v = -u, using sign convention, but distance magnitude is same).
  • Minimum mirror size needed to see full image of a person = Half the person's height.
  • If a mirror is rotated by angle θ, the reflected ray rotates by 2θ.
• Spherical Mirrors (Concave and Convex):
  • Terminology: Pole (P), Centre of Curvature (C), Radius of Curvature (R), Principal Axis, Principal Focus (F), Focal Length (f).
  • Sign Convention (New Cartesian):
    • Distances measured in the direction of incident light are positive; opposite are negative.
    • Heights measured upwards (perpendicular to principal axis) are positive; downwards are negative.
    • All distances are measured from the Pole (P).
  • Relation between f and R: f = R/2 (Focal length is half the radius of curvature). For concave, f and R are negative; for convex, f and R are positive.
  • Mirror Formula: 1/v + 1/u = 1/f
    • u = object distance
    • v = image distance
    • f = focal length
  • Linear Magnification (m): m = (Height of image, h') / (Height of object, h) = -v/u
    • m > 0: Image is virtual and erect.
    • m < 0: Image is real and inverted.
    • |m| > 1: Image is magnified.
    • |m| < 1: Image is diminished.
    • |m| = 1: Image is same size as object.
  • Image Formation Summary: Memorize the table/ray diagrams for image position, nature, and size for different object positions for both concave and convex mirrors. (e.g., Concave: Object at infinity -> Image at F, real, inverted, point-sized; Object between F and P -> Image behind mirror, virtual, erect, magnified. Convex: Always forms virtual, erect, diminished image between P and F).

3. Refraction of Light:

• Bending of light as it passes from one medium to another.
• Laws of Refraction:
  • (i) The incident ray, the refracted ray, and the normal to the interface at the point of incidence all lie in the same plane.
  • (ii) Snell's Law: The ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is constant for a given pair of media and colour of light. sin i / sin r = n₂₁ = n₂ / n₁
    • n₂₁ is the refractive index of medium 2 w.r.t. medium 1.
    • n₁ and n₂ are absolute refractive indices of medium 1 and 2, respectively (n = c/v, where c is speed of light in vacuum, v is speed in medium).
• Apparent Depth: When an object in a denser medium (n₂) is viewed from a rarer medium (n₁), it appears raised. Apparent depth = Real depth * (n₁/n₂) (For viewing from air (n₁≈1) into medium n₂=n, Apparent depth = Real depth / n). Normal Shift = Real Depth - Apparent Depth.
• Total Internal Reflection (TIR):
  • Phenomenon when light travelling from a denser medium to a rarer medium is reflected back into the denser medium.
  • Conditions:
    • Light must travel from a denser to a rarer medium.
    • Angle of incidence (i) must be greater than the critical angle (ic).
  • Critical Angle (ic): The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°. sin ic = n₂ / n₁ (where n₁ > n₂). If rarer medium is air (n₂≈1), sin ic = 1 / n₁.
  • Applications: Mirage, Looming, Brilliance of diamond, Optical fibres, Totally reflecting prisms (used in periscopes, binoculars).

4. Refraction at Spherical Surfaces and by Lenses:

• Refraction at a Single Spherical Surface (from medium n₁ to n₂):
  • Formula: n₂/v - n₁/u = (n₂ - n₁)/R (Remember sign convention).
• Thin Lenses (Convex/Converging, Concave/Diverging):
  • Lens Maker's Formula: (Relates focal length to radii of curvature and refractive index)
    1/f = (n₂/n₁ - 1) * (1/R₁ - 1/R₂)
    • n₂ = refractive index of lens material, n₁ = refractive index of surrounding medium.
    • R₁ and R₂ are radii of curvature of the first and second surfaces, respectively (use sign convention).
    • If surrounding medium is air (n₁=1) and lens material is n (n₂=n): 1/f = (n - 1) * (1/R₁ - 1/R₂)
  • Thin Lens Formula: 1/v - 1/u = 1/f (Similar to mirror formula, but with a minus sign).
  • Linear Magnification (m): m = h'/h = v/u (Note: No minus sign here, unlike mirrors).
  • Power of a Lens (P): Ability to converge or diverge light. P = 1/f (where f is in meters). Unit: Dioptre (D).
    • P is positive for convex lens, negative for concave lens.
  • Combination of Thin Lenses in Contact:
    • Equivalent Focal Length (F): 1/F = 1/f₁ + 1/f₂ + ...
    • Equivalent Power (P): P = P₁ + P₂ + ...
    • Total Magnification (M): M = m₁ * m₂ * ... (for images formed by successive lenses).

5. Refraction through a Prism:

• Angle of Prism (A): Angle between the two refracting faces.
• Angle of Deviation (δ): Angle between the emergent ray and the direction of the incident ray. δ = (i + e) - A (where i=angle of incidence, e=angle of emergence).
• Minimum Deviation (δm): Occurs when i = e. In this condition, the ray passes symmetrically through the prism (r₁ = r₂ = r).
  • i = (A + δm) / 2 and r = A / 2
• Prism Formula (Refractive Index): n₂₁ = n₂/n₁ = sin((A + δm)/2) / sin(A/2)
• Dispersion: Splitting of white light into its constituent colours (VIBGYOR) on passing through a prism. Cause: Refractive index (n) of the prism material is different for different wavelengths (colours) of light (n_violet > n_red). Hence, different colours deviate by different angles (δ_violet > δ_red).
• Angular Dispersion: θ = δ_v - δ_r = (n_v - n_r) A (for small angled prism).
• Dispersive Power (ω): ω = Angular Dispersion / Mean Deviation = (δ_v - δ_r) / δ_y = (n_v - n_r) / (n_y - 1) (where y denotes mean yellow colour). It depends only on the material, not the prism angle.

6. Scattering of Light:

• Absorption and re-emission of light energy by particles (atoms, molecules, dust, water droplets) in the medium.
• Rayleigh Scattering: Scattering by particles much smaller than the wavelength of light (e.g., air molecules). Intensity of scattered light I ∝ 1/λ⁴.
• Applications: Blue colour of the sky (blue light scattered most), Reddish appearance of the sun at sunrise/sunset (less scattered red light reaches observer directly), White clouds (Mie scattering by larger water droplets, scatters all colours almost equally).

7. Optical Instruments:

• Human Eye: Understand basic parts (Cornea, Iris, Pupil, Lens, Retina), accommodation (adjusting focal length), near point (D = 25 cm), far point (infinity). Defects:
  • Myopia (Nearsightedness): Can see near objects, far objects blurry. Image formed in front of retina. Correction: Concave lens.
  • Hypermetropia (Farsightedness): Can see far objects, near objects blurry. Image formed behind retina. Correction: Convex lens.
  • Presbyopia: Age-related loss of accommodation. Correction: Bifocal lenses.
  • Astigmatism: Cornea/Lens has different curvatures in different planes. Correction: Cylindrical lens.
• Microscope: Used to view very small objects.
  • Simple Microscope (Magnifying Glass): Single convex lens.
    • Magnifying Power (Angular Magnification) M:
      • Image at Near Point (D): M = 1 + D/f
      • Image at Infinity (Normal Adjustment): M = D/f
  • Compound Microscope: Two lenses - Objective (short focal length f₀) and Eyepiece (longer focal length fₑ).
    • Magnifying Power M = m₀ * mₑ
      • Image at Infinity (Normal Adjustment): M ≈ (L/f₀) * (D/fₑ) (L = tube length ≈ distance between objective and eyepiece focal points).
      • Image at Near Point (D): M ≈ -(L/f₀) * (1 + D/fₑ) (Negative sign indicates inverted final image).
• Telescope: Used to view distant objects.
  • Astronomical Telescope (Refracting): Objective (large aperture, long focal length f₀) and Eyepiece (small aperture, short focal length fₑ).
    • Magnifying Power M:
      • Image at Infinity (Normal Adjustment): M = -f₀/fₑ. Length L = f₀ + fₑ.
      • Image at Near Point (D): M = -(f₀/fₑ) * (1 + fₑ/D). Length L = f₀ + uₑ.
    • (Negative sign indicates inverted final image).
  • Reflecting Telescope (e.g., Cassegrain): Uses mirrors (usually parabolic primary) instead of lenses for the objective.
    • Advantages: No chromatic aberration, no spherical aberration (if parabolic mirror used), larger light-gathering power, lighter support structure.

Key Formulas Summary:

• Mirror: 1/v + 1/u = 1/f, m = -v/u
• Refraction at Spherical Surface: n₂/v - n₁/u = (n₂ - n₁)/R
• Lens Maker's: 1/f = (n₂/n₁ - 1) * (1/R₁ - 1/R₂)
• Thin Lens: 1/v - 1/u = 1/f, m = v/u
• Power: P = 1/f (f in m)
• Combination (Lens): 1/F = 1/f₁ + 1/f₂, P = P₁ + P₂
• Prism: n = sin((A + δm)/2) / sin(A/2)
• Critical Angle: sin ic = n₂ / n₁ (n₁ > n₂)
• Microscope (Compound, Normal Adj.): M ≈ (L/f₀) * (D/fₑ)
• Telescope (Astronomical, Normal Adj.): M = -f₀/fₑ

Remember to use the sign convention consistently while solving numerical problems. Practice drawing ray diagrams for mirrors, lenses, microscopes, and telescopes.

Multiple Choice Questions (MCQs):

1. A concave mirror produces a real, inverted image of the same size as the object. The object must be placed:
   (a) At the focus (F)
   (b) At the centre of curvature (C)
   (c) Between F and C
   (d) Beyond C

2. Light travels from air into glass (refractive index 1.5). If the angle of incidence is 60°, what is the approximate angle of refraction? (sin 60° ≈ 0.866)
   (a) 30°
   (b) 35°
   (c) 45°
   (d) 60°

3. The phenomenon responsible for the brilliance of a diamond is:
   (a) Diffraction
   (b) Interference
   (c) Total Internal Reflection
   (d) Scattering

4. A thin convex lens of focal length 10 cm is placed in contact with a thin concave lens of focal length 20 cm. The focal length of the combination is:
   (a) +10 cm
   (b) -10 cm
   (c) +20 cm
   (d) -20 cm

5. In Rayleigh scattering, the intensity of scattered light is proportional to:
   (a) λ
   (b) λ²
   (c) 1/λ²
   (d) 1/λ⁴

6. A person suffering from Myopia (nearsightedness) requires which type of lens for correction?
   (a) Convex lens
   (b) Concave lens
   (c) Cylindrical lens
   (d) Bifocal lens

7. For a prism, the angle of minimum deviation (δm) is equal to the angle of the prism (A). The refractive index of the prism material could be: (Assume small angle prism approximation is not valid here)
   (a) √2
   (b) 1.5
   (c) √3
   (d) 2

8. In a compound microscope, the intermediate image formed by the objective lens is:
   (a) Real, inverted, and magnified
   (b) Virtual, erect, and magnified
   (c) Real, erect, and diminished
   (d) Virtual, inverted, and diminished

9. An optical fibre works on the principle of:
   (a) Refraction
   (b) Scattering
   (c) Total Internal Reflection
   (d) Interference

10. The power of a plane glass slab is:
    (a) Zero
    (b) Infinite
    (c) Positive
    (d) Negative

Answers to MCQs:

1. (b) At the centre of curvature (C)
2. (b) 35° (Using Snell's Law: 1 * sin 60° = 1.5 * sin r => sin r = 0.866 / 1.5 ≈ 0.577 => r ≈ 35°)
3. (c) Total Internal Reflection
4. (c) +20 cm (P₁ = 1/0.1 = +10 D, P₂ = 1/(-0.2) = -5 D. P = P₁ + P₂ = +5 D. F = 1/P = 1/5 m = 0.2 m = +20 cm)
5. (d) 1/λ⁴
6. (b) Concave lens
7. (c) √3 (Given δm = A. Using prism formula, n = sin((A+A)/2) / sin(A/2) = sin(A) / sin(A/2) = (2 sin(A/2)cos(A/2)) / sin(A/2) = 2 cos(A/2). If A=60°, n = 2 cos(30°) = 2 * (√3/2) = √3. This is a possible value.)
8. (a) Real, inverted, and magnified
9. (c) Total Internal Reflection
10. (a) Zero (A plane glass slab does not converge or diverge parallel rays, focal length is infinite, hence power is zero).

Study these notes thoroughly, understand the concepts behind the formulas, and practice numerical problems. All the best for your exams!