Class 12 Physics Chapter 9: Ray Optics and Optical Instruments | Full Notes & Formulas

📅 Tuesday, 20 January 2026 📖 3-5 min read
Class 12 Physics • NCERT

Chapter 9: Ray Optics

Complete Textbook Edition (Reflection, Refraction, Lenses & Instruments)

Vol 1: Reflection of Light & Spherical Mirrors

Light: Electromagnetic radiation that produces the sensation of vision ($\lambda \approx 400 \text{ nm to } 750 \text{ nm}$).
Ray Optics Assumption: Light travels in straight lines (Rectilinear Propagation) because the wavelength of light is much smaller than the size of common objects.

1. Spherical Mirrors

  • Focal Length ($f$): The distance between Pole (P) and Focus (F). For spherical mirrors with small aperture, $f = R/2$.
  • Sign Convention:
    • All distances measured from Pole.
    • Direction of incident light is Positive (+). Opposite direction is Negative (-).
    • Heights upwards are (+), downwards are (-).
Mirror Formula:

$$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$

Magnification ($m$):
$$m = \frac{h'}{h} = - \frac{v}{u}$$

Vol 2: Refraction & Total Internal Reflection

Refraction: The bending of light when it passes from one transparent medium to another.

1. Laws of Refraction

Snell's Law: The ratio of sine of angle of incidence to sine of angle of refraction is constant.

$$\frac{\sin i}{\sin r} = \frac{n_2}{n_1} = n_{21}$$

2. Total Internal Reflection (TIR)

When light travels from Denser to Rarer medium and angle of incidence $i > i_c$ (Critical Angle), the ray reflects back into the same medium.

Condition for Critical Angle ($i_c$):

$$\sin i_c = \frac{1}{n}$$
(Where $n$ is refractive index of denser medium w.r.t air)

Applications of TIR:
1. Optical Fibers: Transmission of light/data with negligible loss.
2. Mirage: Optical illusion in deserts.
3. Prisms: Used to invert images ($90^\circ, 180^\circ$ prisms).

Vol 3: Refraction at Spherical Surfaces & Lenses

1. Lens Maker's Formula (5 Marks Derivation)

This formula relates focal length to the refractive index and radii of curvature.

$$\frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$$

2. Thin Lens Formula & Power

Lens Formula:
$$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$
Power of Lens ($P$):
$$P = \frac{1}{f(\text{in meters})}$$
Unit: Diopter (D)

Combination of Lenses: If two thin lenses are in contact, effective power $P = P_1 + P_2$.

Vol 4: Prism & Dispersion

Dispersion: Splitting of white light into its constituent colors (VIBGYOR). Cause: Refractive index varies with wavelength ($\lambda$).

Prism Formula

At minimum deviation ($\delta_m$), the ray passes symmetrically through the prism ($i=e$).

$$n = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}$$

Rainbow: A natural phenomenon caused by Dispersion, Refraction, and Internal Reflection of sunlight by water droplets.

Vol 5: Optical Instruments

1. Compound Microscope

Uses two convex lenses: Objective (small aperture/focal length) and Eyepiece (larger aperture/focal length).

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Magnifying Power ($m$):
$$m \approx \frac{L}{f_o} \left( 1 + \frac{D}{f_e} \right)$$
(Where $L$ is tube length, $D$ is least distance of distinct vision $\approx 25$ cm).

2. Astronomical Telescope

Objective has large aperture (to gather light) and large focal length.

Magnifying Power (Normal Adjustment):
$$m = \frac{f_o}{f_e}$$

Vol 6: Mission 100 Question Bank

Section A: MCQs

Q1. A convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens. Its focal length will:
(a) Become zero   (b) Become infinite   (c) Remain unchanged   (d) Become small
Ans: (b) Become infinite (It acts as a plane glass sheet).

Q2. For total internal reflection to occur, light must travel from:
(a) Rarer to Denser medium   (b) Denser to Rarer medium
(c) Any medium   (d) Vacuum to Air
Ans: (b) Denser to Rarer medium.

Section B: Numericals (Important)

Q3. A double convex lens is made of glass of refractive index 1.55, with both faces of the same radius of curvature. Find the radius of curvature required if the focal length is to be 20 cm.

Solution:
Given: $f = 20$ cm, $n = 1.55$, $R_1 = R, R_2 = -R$.
Using Lens Maker's Formula:
$\frac{1}{f} = (n-1) (\frac{1}{R} - \frac{1}{-R})$
$\frac{1}{20} = (0.55) (\frac{2}{R})$
$\frac{1}{20} = \frac{1.1}{R} \Rightarrow R = 22$ cm.
Ans: 22 cm.

Section C: Conceptual

Q4. Why does the sky appear blue?
Ans: Due to Scattering of light. According to Rayleigh's law, scattering $\propto 1/\lambda^4$. Blue light has shorter wavelength, so it scatters much more than red light.

Mission 100 Physics Series

Next Chapter: Wave Optics (Interference, Diffraction & Polarization)!

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