Ray Optics and Optical Instruments Formula Sheet is designed for Class 12 Physics (CBSE 2025–26) and NEET/JEE aspirants. It includes all important formulas from reflection, refraction, mirror and lens equations, magnification, prism deviation, total internal reflection, and optical instruments. Each formula is presented with clear meaning, SI units, and simple context for quick revision before exams.
Ray Optics and Optical Instruments Formula Sheet
Ray Optics deals with the straight-line propagation of light and its interaction with reflective and refractive surfaces. This simplified model helps understand how images form through mirrors, lenses, and optical instruments.
- Reflection: Bouncing back of light from a surface.
- Refraction: Bending of light as it travels from one medium to another of different optical densities.
- Total Internal Reflection (TIR): Complete reflection within a denser medium beyond the critical angle.
- Optical Instruments: Include human eye, microscopes, telescopes, cameras, and periscopes—all based on refraction and reflection principles.
Comprehensive Formula Sheet
The table below lists all key formulas for Ray Optics and Optical Instruments—useful for both theory-based and numerical questions.
| Concept | Formula | Remarks / Usage |
|---|---|---|
| Law of Reflection | \( \angle i = \angle r \) | Incident and reflected angles are equal. |
| Snell’s Law | \( n_1\sin i = n_2\sin r \) | Used to calculate refractive index between two media. |
| Refractive Index | \( n = \frac{c}{v} \) | Speed of light in vacuum divided by its speed in medium. |
| Critical Angle | \( \sin i_c = \frac{n_2}{n_1} \) | At this angle, refraction grazes the surface. |
| Mirror Formula | \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \) | For concave/convex mirrors; follow sign convention. |
| Lens Formula | \( \frac{1}{f} = \frac{1}{v} – \frac{1}{u} \) | For convex/concave lenses; “u” is always taken from optical center. |
| Magnification (Mirror) | \( m = \frac{-v}{u} \) | Negative sign indicates inverted image. |
| Magnification (Lens) | \( m = \frac{v}{u} \) | Used for both convex and concave lenses. |
| Power of Lens | \( P = \frac{1}{f(\text{\in m})} \) | Unit: Dioptre (D); +ve for convex, –ve for concave lenses. |
| Lens Maker’s Formula | \( \frac{1}{f} = (n-1)\left(\frac{1}{R_1} – \frac{1}{R_2}\right) \) | Design equation for lenses; R₁ and R₂ are radii of curvature. |
| Combination of Lenses | \( \frac{1}{f_{eq}} = \frac{1}{f_1} + \frac{1}{f_2} \) | Used when lenses are in contact. |
| Magnifying Power of Simple Microscope | \( M = 1 + \frac{D}{f} \) | D = least distance of distinct vision (25 cm). |
| Magnifying Power of Compound Microscope | \( M = \frac{v}{u_o}\left(1 + \frac{D}{f_e}\right) \) | Product of magnifications of objective and eyepiece lenses. |
| Magnifying Power of Telescope | \( M = \frac{f_o}{f_e} \) | For astronomical telescopes under normal adjustment. |
| Deviation in Prism | \( \delta = (i_1 + i_2) – A \) | Angle of deviation; A = prism angle. |
| Minimum Deviation Condition | \( n = \frac{\sin\left(\frac{A + D_{\min}}{2}\right)}{\sin\left(\frac{A}{2}\right)} \) | At Dₘᵢₙ, angle of incidence = angle of emergence. |
Key Derivations Explained Step-by-Step
1. Mirror Formula Derivation:
Using geometry and similar triangles for concave mirror:
\(\frac{AB}{A’B’} = \frac{BO}{B’O}\). Simplifying gives \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \).
2. Lens Maker’s Formula:
For refraction at two spherical surfaces, applying Snell’s Law twice gives \( \frac{1}{f} = (n-1)\left(\frac{1}{R_1} – \frac{1}{R_2}\right) \).
3. Prism Deviation:
From refraction geometry: \( \delta = i_1 + i_2 – A \). At minimum deviation, \( i_1 = i_2 \), hence \( n = \frac{\sin\left(\frac{A + D_{\min}}{2}\right)}{\sin\left(\frac{A}{2}\right)} \).
4. Total Internal Reflection (TIR):
At critical angle, refracted ray grazes boundary (\(r=90°\)), hence \( \sin i_c = \frac{n_2}{n_1} \).
Practical Applications of Formulas
- Optical Fibre Communication: Uses TIR formula to maintain light transmission without loss.
- Eye Defect Correction: Uses power formula \( P = 1/f \) to design concave/convex lenses for spectacles.
- Microscope Design: Uses combined magnification formula \( M = \frac{v}{u_o}\left(1+\frac{D}{f_e}\right) \).
- Telescope Engineering: Applies \( M = f_o / f_e \) for astronomical instruments.
- Prism & Dispersion Studies: Apply deviation formula to measure refractive index of materials.
Worked Examples (Exam-Oriented)
Example 1: Calculate focal length of a double convex lens with R₁ = 20 cm, R₂ = 30 cm, n = 1.5.
Using Lens Maker’s Formula:
\(\frac{1}{f} = (1.5 – 1)\left(\frac{1}{20} – \frac{1}{-30}\right) = 0.5\left(\frac{1}{20} + \frac{1}{30}\right) = 0.5\times\frac{5}{60} = \frac{1}{24}\).
Hence \( f = 24\,\text{cm} \).
Example 2: For a microscope with fₒ = 2 cm, fₑ = 5 cm, object distance uₒ = 2.1 cm, and D = 25 cm, find total magnification.
\( M = \frac{v}{u_o}\left(1+\frac{D}{f_e}\right) \approx \frac{2}{2.1}(1+\frac{25}{5}) = 0.95 \times 6 = 5.7 \).
So the microscope gives ≈ 5.7× magnification.