Formula Bank & Dimensional Analysis
All formulas organized and searchable - your exam cheat sheet (legal!)
How to use this page: Don't just memorize - understand when to apply which formula. Each formula is tagged with difficulty and exam relevance.
Spherical Mirrors
Mirror Formula
Most important formula. Remember the PLUS sign.
Focal Length
Focal length is half radius of curvature.
Magnification
Negative sign is crucial. Negative m = inverted image.
Power
Unit: Dioptre (D). Concave: P < 0, Convex: P > 0
70% errors happen in sign convention. For mirrors: distances measured from pole, object side is negative.
Spherical Lenses
Lens Formula
MINUS sign differentiates from mirror formula.
Lens Maker's Formula
Derivation asked frequently in CBSE boards.
Magnification
No negative sign for lenses (unlike mirrors).
Power
Converging: P > 0, Diverging: P < 0
Lenses in Contact
1/f = 1/f₁ + 1/f₂
Powers add algebraically. High scoring topic.
Lenses Separated
d = separation between lenses.
JEE Twist: When lens is in liquid, use: 1/f_liquid = (n_lens/n_liquid - 1)(1/R₁ - 1/R₂)
Refraction Formulas
Snell's Law
Foundation of all refraction problems.
Refractive Index
Frequency remains constant in refraction.
Critical Angle
Only for denser to rarer medium.
Apparent Depth
Shift = d(1 - 1/n)
NEET favorite numerical problem.
Single Surface Refraction
Used in lens maker's formula derivation.
Prism Formulas
Prism Relations
δ = i + e - A
A = prism angle, δ = deviation angle
At Minimum Deviation
i = e, r₁ = r₂ = A/2
Used to find RI of prism material.
Dispersion
ω = (nᵥ - nᵣ)/(n - 1)
θ = angular dispersion, ω = dispersive power
Small Angle Approximation
Valid when A and i are very small.
For minimum deviation, ray inside prism is parallel to base. Symmetric ray path makes calculations easier.
Optical Instruments
Simple Microscope
Image at Near Point
D = 25 cm (near point of normal eye)
Image at Infinity
More comfortable viewing (relaxed eye)
Compound Microscope
Total Magnification (at D)
≈ -(L/f₀)(1 + D/fₑ)
L = tube length = v₀ + fₑ
Total Magnification (at ∞)
≈ -(L/f₀)(D/fₑ)
More comfortable for long viewing
Astronomical Telescope
Normal Adjustment (at ∞)
L = f₀ + fₑ
f₀ >> fₑ for high magnification
Image at Near Point
where uₑ found from lens formula
Resolving Power
Microscope
n = RI of medium between object and objective
Telescope
a = aperture diameter
High Scoring: Microscope and telescope magnification formulas are asked in 90% of papers. Memorize all forms.
Dimensional Analysis
| Quantity | Dimensions | SI Unit |
|---|---|---|
| Focal Length (f) | [L] | meter (m) |
| Power (P) | [L⁻¹] | Dioptre (D) = m⁻¹ |
| Refractive Index (n) | [M⁰L⁰T⁰] | dimensionless |
| Magnification (m) | [M⁰L⁰T⁰] | dimensionless |
| Angles (all) | [M⁰L⁰T⁰] | radian (rad) |
| Wavelength (λ) | [L] | meter (m) |
JEE Main may ask: "Which quantity is dimensionless?" Answer: n, m, angular magnification, relative RI.
Quick Formula Summary Table
| Topic | Key Formula | When to Use |
|---|---|---|
| Mirrors | 1/f = 1/v + 1/u | Finding image position for any mirror |
| Lenses | 1/f = 1/v - 1/u | Finding image position for any lens |
| Refraction | n₁ sin i = n₂ sin r | Light crossing medium boundary |
| TIR | sin θc = 1/n | Finding critical angle (denser to rarer) |
| Prism (min dev) | n = sin[(A+δₘ)/2] / sin(A/2) | Finding RI of prism material |
| Microscope | m = -(L/f₀)(1 + D/fₑ) | Compound microscope magnification |
| Telescope | m = -f₀/fₑ | Angular magnification in normal adjustment |