class 12 notes

Class 12 Physics Notes Chapter 9 (Ray Optics and Optical Instruments) – Examplar Problems (English) Book

Philoid

Philoid

— 8 min read

Examplar Problems (English)
Alright class, let's get straight into Chapter 9: Ray Optics and Optical Instruments. This is a crucial chapter, not just for your board exams but heavily featured in various government competitive exams. We'll focus on the core concepts, formulas, and applications you absolutely need to know. Pay close attention to sign conventions – they are key to solving numerical problems correctly.

Chapter 9: Ray Optics and Optical Instruments - Detailed Notes

1. Introduction:

  • Ray Optics (or Geometrical Optics) treats light as travelling in straight lines called rays.
  • It explains phenomena like reflection, refraction, image formation by mirrors and lenses, and the working of optical instruments.
  • A 'ray' indicates the path of energy propagation. A 'beam' is a bundle of rays.

2. Reflection of Light:

  • The bouncing back of light into the same medium after striking a surface.
  • Laws of Reflection:
    • The incident ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane.
    • The angle of incidence (i) equals the angle of reflection (r). (∠i = ∠r)
  • Reflection from Plane Mirrors:
    • Image formed is virtual, erect, laterally inverted, same size as the object, and as far behind the mirror as the object is in front.
    • Focal length of a plane mirror is infinity.
  • Reflection from Spherical Mirrors (Concave & Convex):
    • Terminology: Pole (P), Centre of Curvature (C), Radius of Curvature (R), Principal Axis, Principal Focus (F), Focal Length (f).
    • Relation: f = R/2
    • Sign Convention (New Cartesian Sign Convention):
      1. All distances are measured from the Pole (P).
      2. Distances measured in the direction of incident light are positive; opposite direction is negative.
      3. Heights measured upwards perpendicular to the principal axis are positive; downwards are negative.
      4. Consequence: For standard setups (object on the left):
        • u (object distance) is always negative.
        • f is negative for concave mirrors, positive for convex mirrors.
        • R is negative for concave mirrors, positive for convex mirrors.
        • v (image distance) is negative for real images (in front), positive for virtual images (behind).
    • Mirror Formula: Relates object distance (u), image distance (v), and focal length (f).
      1/v + 1/u = 1/f
    • Linear Magnification (m): Ratio of the height of the image (h') to the height of the object (h).
      m = h'/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 the same size.
    • Image Formation: Ray diagrams are essential (practice drawing them for different object positions for both concave and convex mirrors).

3. Refraction of Light:

  • The bending of light as it passes obliquely from one transparent medium to another.
  • Cause: Change in the speed of light in different media.
  • Laws of Refraction (Snell's Law):
    • The incident ray, the refracted ray, and the normal to the interface at the point of incidence all lie in the same plane.
    • 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. This constant is the refractive index of the second medium with respect to the first (n₂₁).
      n₂₁ = sin i / sin r = n₂ / n₁ = v₁ / v₂
      where n₁ and n₂ are absolute refractive indices, v₁ and v₂ are speeds of light in medium 1 and 2 respectively.
  • Absolute Refractive Index (n): n = c/v (where c is speed of light in vacuum, v is speed in medium). n ≥ 1.
  • Apparent Depth: When an object in a denser medium is viewed from a rarer medium, it appears raised.
    • Real Depth / Apparent Depth = n (of denser medium w.r.t rarer medium)
  • Total Internal Reflection (TIR):
    • Condition 1: Light must travel from a denser medium to a rarer medium.
    • Condition 2: 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 the rarer medium is air/vacuum (n₂ ≈ 1), then sin ic = 1 / n₁.
    • Applications: Brilliance of diamonds, mirages, optical fibres, totally reflecting prisms.

4. Refraction at Spherical Surfaces and by Lenses:

  • Refraction at a Spherical Surface (Single Surface):
    • Formula relating u, v, R, n₁, n₂ (light travels from medium n₁ to n₂):
      n₂/v - n₁/u = (n₂ - n₁)/R
      (Apply sign convention carefully for u, v, R).
  • Lenses: A transparent medium bounded by two surfaces, at least one of which is spherical.
    • Types: Convex (converging) and Concave (diverging).
    • Terminology: Optical Centre (O), Principal Axis, Principal Foci (F₁, F₂), Focal Length (f).
    • Sign Convention (Similar to mirrors, but distances measured from Optical Centre O):
      1. All distances measured from O.
      2. Direction of incident light: positive; opposite: negative.
      3. Heights upwards: positive; downwards: negative.
      4. Consequence: For standard setups (object on the left):
        • u is always negative.
        • f is positive for convex lenses, negative for concave lenses.
        • R₁, R₂ depend on the surface curvature relative to O.
        • v is positive for real images (right side), negative for virtual images (left side).
    • Lens Maker's Formula: Relates f, refractive index of lens material (n₂), surrounding medium (n₁), and radii of curvature (R₁, R₂).
      1/f = (n₂/n₁ - 1) * (1/R₁ - 1/R₂)
      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: Relates u, v, and f for a thin lens.
      1/v - 1/u = 1/f
    • Linear Magnification (m):
      m = h'/h = v/u
      (Note: No negative sign here, unlike mirrors). Interpretation of m (sign, magnitude) is the same as for mirrors.
    • Power of a Lens (P): Ability to converge or diverge light. Measured in Dioptres (D).
      P = 1/f  (where f is in meters)
      • 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 + ...
      • Magnification (M): M = m₁ * m₂ * ... (for the combination)

5. Refraction through a Prism:

  • Angle of Deviation (δ): The 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, A=angle of prism)
  • Minimum Deviation (δm): Occurs when i = e. In this case, the ray passes symmetrically through the prism (r₁ = r₂ = r).
    • r = A/2
    • i = (A + δm) / 2
    • Prism Formula: Relates refractive index (n) of the prism material to A and δm.
      n = 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) depends on wavelength (λ). n is highest for violet, lowest for red. n_v > n_r. Therefore, violet deviates the most, red deviates the least.

6. Scattering of Light:

  • Process by which particles (like air molecules, dust, water droplets) absorb light energy and re-emit it in different directions.
  • Rayleigh Scattering: Scattering intensity (I) is inversely proportional to the fourth power of the wavelength (λ). I ∝ 1/λ⁴.
  • Applications: Blue colour of the sky (blue light scattered more than red), reddish appearance of the sun at sunrise/sunset (most blue is scattered away, red reaches observer).

7. Optical Instruments:

  • Human Eye: (Basic structure and function - cornea, lens, retina, accommodation, defects like myopia, hypermetropia and their correction using lenses).
  • Microscope: Used to view very small objects.
    • Simple Microscope (Magnifying Glass): A single convex lens.
      • Magnifying Power (M):
        • Image at Near Point (D=25 cm): M = 1 + D/f
        • Image at Infinity (Normal Adjustment): M = D/f
    • Compound Microscope: Uses two lenses - Objective (short focal length f₀) and Eyepiece (longer focal length fe).
      • Objective forms a real, inverted, magnified intermediate image. Eyepiece acts as a simple magnifier for this intermediate image.
      • Magnifying Power (M): (L = tube length ≈ distance between objective's second focus and eyepiece's first focus)
        • Image at Near Point: M ≈ (L/f₀) * (1 + D/fe) or M = m₀ * me = (-v₀/u₀) * (1 + D/fe)
        • Image at Infinity (Normal Adjustment): M ≈ (L/f₀) * (D/fe) or M = m₀ * me = (-v₀/u₀) * (D/fe)
      • Overall magnification is negative (inverted final image).
  • Telescope: Used to view distant objects (stars, planets).
    • Refracting Telescope (Astronomical): Uses two convex lenses - Objective (large aperture, long focal length f₀) and Eyepiece (small aperture, short focal length fe).
      • Objective forms a real, inverted image at or near its focus. Eyepiece magnifies this image.
      • Magnifying Power (M):
        • Image at Infinity (Normal Adjustment): M = -f₀/fe (Length of telescope L = f₀ + fe)
        • Image at Near Point: M = -f₀/fe * (1 + fe/D) (Length of telescope L = f₀ + ue)
      • Negative sign indicates inverted final image.
    • Reflecting Telescope: Uses a concave mirror as the objective (e.g., Cassegrain).
      • Advantages over Refracting: No chromatic aberration, no spherical aberration (if parabolic mirror used), larger light-gathering power, easier to support large mirrors.

Multiple Choice Questions (MCQs):

  1. A ray of light is incident on a plane mirror at an angle of 30° with the mirror surface. The angle of reflection will be:
    a) 30°
    b) 60°
    c) 90°
    d) 0°

  2. An object is placed 20 cm in front of a concave mirror of focal length 10 cm. The image formed is:
    a) Real, inverted, and same size
    b) Real, inverted, and magnified
    c) Virtual, erect, and magnified
    d) Real, inverted, and diminished

  3. Light travels from air (n≈1) into glass (n=1.5). If the angle of incidence is 45°, what is the approximate angle of refraction? (sin 45° ≈ 0.707)
    a) 28° (sin 28° ≈ 0.47)
    b) 45°
    c) 60° (sin 60° ≈ 0.866)
    d) 90°

  4. Which phenomenon is responsible for the working of optical fibres?
    a) Reflection
    b) Refraction
    c) Total Internal Reflection
    d) Dispersion

  5. A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length 10 cm. The power of the combination in Dioptres is:
    a) +5 D
    b) -5 D
    c) +15 D
    d) -15 D

  6. A biconvex lens has radii of curvature 20 cm each. If the refractive index of the material of the lens is 1.5, its focal length is:
    a) 10 cm
    b) 20 cm
    c) 5 cm
    d) Infinity

  7. For a prism of angle A = 60°, the angle of minimum deviation is 30°. The refractive index of the material of the prism is:
    a) √2
    b) 1.5
    c) √3
    d) 2

  8. The blue colour of the sky is due to:
    a) Reflection of light
    b) Refraction of light
    c) Dispersion of light
    d) Scattering of light

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

  10. For an astronomical telescope in normal adjustment (final image at infinity), the separation between the objective and eyepiece is (f₀ = focal length of objective, fe = focal length of eyepiece):
    a) f₀ / fe
    b) f₀ * fe
    c) f₀ - fe
    d) f₀ + fe

Answers to MCQs:

  1. b (Angle of incidence is with normal, so i = 90° - 30° = 60°. Angle r = i = 60°)
  2. a (u=-20cm, f=-10cm. 1/v = 1/f - 1/u = 1/(-10) - 1/(-20) = -1/10 + 1/20 = -1/20. So v=-20cm. m = -v/u = -(-20)/(-20) = -1. Real, inverted, same size)
  3. a (n₁ sin i = n₂ sin r => 1 * sin 45° = 1.5 * sin r => sin r = sin 45° / 1.5 ≈ 0.707 / 1.5 ≈ 0.47. r ≈ 28°)
  4. c (Total Internal Reflection)
  5. b (P₁ = 1/f₁ = 1/0.20 = +5 D. P₂ = 1/f₂ = 1/(-0.10) = -10 D. P = P₁ + P₂ = 5 - 10 = -5 D)
  6. b (Using Lens Maker's: 1/f = (n-1)(1/R₁ - 1/R₂). Here n=1.5, R₁=+20cm, R₂=-20cm. 1/f = (1.5-1)(1/20 - 1/(-20)) = 0.5 * (1/20 + 1/20) = 0.5 * (2/20) = 0.5 * (1/10) = 1/20. So f = 20 cm)
  7. a (n = sin((A+δm)/2) / sin(A/2) = sin((60+30)/2) / sin(60/2) = sin(45°) / sin(30°) = (1/√2) / (1/2) = 2/√2 = √2)
  8. d (Scattering of light by atmospheric particles, Rayleigh scattering)
  9. c (Real, inverted, and magnified)
  10. d (In normal adjustment, L = f₀ + fe)

Make sure you revise these concepts thoroughly, practice numerical problems using the formulas and sign conventions, and understand the working principles of the optical instruments. Good luck!

Read more