NCERT Solutions for Class 12 Physics Chapter 9 Ray Optics and Optical Instruments
NCERT Solutions for Class 12 Physics Chapter 9 Ray Optics and Optical Instruments provides comprehensive topic notes, core optical formulas, lens and mirror formulas, total internal reflection, prism dispersion, and complete ray diagram analyses for microscopes and telescopes.
Overview of Topics & Subtopics (Click to Jump)
1. Reflection, Refraction & Total Internal Reflection
Short Note:
• Mirror Formula: 1 / f = 1 / v + 1 / u, where focal length f = R / 2 and linear magnification m = -v / u = h' / h.
• Laws of Refraction (Snell's Law): n₁ sin i = n₂ sin r => Refractive index n₂₁ = n₂ / n₁ = c / v = λ₁ / λ₂.
• Apparent Depth: Real Depth / Apparent Depth = n. Apparent shift Δx = t (1 - 1 / n).
• Total Internal Reflection (TIR): When light travels from denser to rarer medium at an angle of incidence greater than critical angle i_c.
- Critical Angle Condition: sin i_c = 1 / n.
- Applications: Optical fibers, mirage formation, sparkling of diamonds, and totally reflecting prisms.
2. Refraction at Spherical Surfaces, Lenses & Prisms
Short Note:
• Refraction at a Single Spherical Surface: n₂ / v - n₁ / u = (n₂ - n₁) / R.
• Lens Maker's Formula: 1 / f = (n - 1) × (1 / R₁ - 1 / R₂).
• Thin Lens Formula: 1 / f = 1 / v - 1 / u => Magnification m = v / u = h' / h.
• Power of Lens (P): Reciprocal of focal length in meters: P = 1 / f(m) (Unit: Dioptre, D).
- Combination of thin lenses in contact: 1 / F = 1 / f₁ + 1 / f₂ and P = P₁ + P₂.
• Refraction through Prism: Angle of deviation δ = i + e - A.
- At Minimum Deviation (δ_m): i = e and r₁ = r₂ = A / 2.
- Prism Refractive Index Formula: n = sin[(A + δ_m) / 2] / sin(A / 2).
3. Optical Instruments (Microscopes & Telescopes)
Short Note:
• Simple Microscope (Magnifying Glass):
- Image at Near Point (D = 25 cm): m = 1 + D / f.
- Image at Infinity (Normal Adjustment): m = D / f.
• Compound Microscope: Consists of objective (small f_o & aperture) and eyepiece (larger f_e).
- Magnifying Power (Image at D): m = m_o × m_e ≈ -(L / f_o) × (1 + D / f_e).
- Magnifying Power (Image at ∞): m = -(L / f_o) × (D / f_e).
• Astronomical Telescope (Refracting Type): Consists of objective (large f_o & aperture) and eyepiece (small f_e).
- Normal Adjustment (Image at ∞): m = -f_o / f_e and Tube Length L = f_o + f_e.
- Image at Near Point (D): m = -(f_o / f_e) × (1 + f_e / D).
• Reflecting Telescope (Cassegrain Type): Uses parabolic primary mirror instead of lens. Advantages: Free from chromatic and spherical aberration, higher light gathering power.
Intext & Conceptual Questions
• Definition: Total Internal Reflection is the optical phenomenon in which a ray of light travelling from an optically denser medium to a rarer medium is completely reflected back into the denser medium at the interface when the angle of incidence exceeds the critical angle.
• Conditions required for TIR:
1. Light must travel from an optically denser medium to a rarer medium.
2. The angle of incidence in the denser medium must be greater than the critical angle (i > i_c) for the given pair of media.
• Mathematical Relation: sin i_c = 1 / n (or n = 1 / sin i_c), where n is the refractive index of denser medium with respect to rarer medium.
| Feature | Compound Microscope | Astronomical Telescope |
|---|---|---|
| Objective Lens | Very small focal length (f_o) and small aperture. | Large focal length (f_o) and large aperture. |
| Eyepiece Lens | Focal length (f_e) is larger than objective lens. | Focal length (f_e) is smaller than objective lens. |
| Object Distance | Object is placed just beyond focal point of objective. | Object is at very large/infinite distance. |
| Magnification Formula | m ≈ -(L / f_o) × (D / f_e) | m = -f_o / f_e |
| Primary Purpose | To observe highly magnified images of tiny near objects. | To observe angularly magnified views of distant heavenly bodies. |
Textbook Chapter End Exercise Questions
Given:
• Size of object (h) = +2.5 cm
• Object distance (u) = -27 cm
• Radius of curvature (R) = -36 cm => Focal length (f) = R / 2 = -18 cm
Step 1: Calculate Image Distance (v) using Mirror Formula
1 / f = 1 / v + 1 / u
1 / (-18) = 1 / v + 1 / (-27)
1 / v = 1 / 27 - 1 / 18 = (2 - 3) / 54 = -1 / 54
v = -54 cm
The screen should be placed at a distance of 54 cm in front of the mirror.
Step 2: Calculate Height of Image (h')
m = h' / h = -v / u
h' / 2.5 = -(-54) / (-27) = -2
h' = -2 × 2.5 = -5.0 cm
• The image distance is 54 cm (real image on object side).
• The height of the image is 5.0 cm (inverted and magnified).
Given:
• Real depth (h) = 12.5 cm
• Apparent depth in water (h'_w) = 9.4 cm
Part (a): Refractive Index of Water (n_w)
n_w = Real Depth / Apparent Depth = 12.5 / 9.4 ≈ 1.33
Part (b): Apparent depth in new liquid (n_l = 1.63)
h'_l = Real Depth / n_l = 12.5 / 1.63 ≈ 7.67 cm
Step 3: Calculate Shift Distance for Microscope
Shift = Apparent depth in water - Apparent depth in liquid
Shift = 9.4 - 7.67 = 1.73 cm
• The refractive index of water is 1.33.
• The microscope must be moved up by 1.73 cm to focus on the needle again.
Read More & Chapter Resources
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