Optics
Complete Formula Sheet & Shortcut Bible · BITSAT 2026
CrackIt
Reflection & Refraction Fundamentals
Snell's Law
n₁ sin i = n₂ sin r
Relates angles of incidence (i) and refraction (r) for light passing between media with refractive indices n₁ and n₂.
Refractive Index (n)
n = c / v
Ratio of speed of light in vacuum (c) to speed in the medium (v). Always n ≥ 1.
Critical Angle (θc)
sin θc = n₂ / n₁
For Total Internal Reflection (TIR). Light must travel from denser (n₁) to rarer (n₂) medium.
Apparent Depth
d_app = d_real / n
How deep an object in a medium (n) appears from outside. Object appears raised.
Refraction at Spherical Surface
n₂/v - n₁/u = (n₂-n₁)/R
Sign convention is crucial. R is positive for convex surface.
Mirrors & Lenses
Mirror Formula
1/f = 1/v + 1/u
f is +ve for concave, -ve for convex mirrors. (Using f = -R/2 convention)
Lens Formula
1/f = 1/v - 1/u
f is +ve for convex lens, -ve for concave lens.
Magnification (m)
m = hᵢ/h₀ = -v/u
For both lenses and mirrors. m > 0 for virtual/erect, m < 0 for real/inverted.
Lens Maker's Formula
1/f = (n₂/n₁ - 1)(1/R₁ - 1/R₂)
n₂ is lens material, n₁ is surrounding medium. R₁, R₂ are radii of curvature.
Power of a Lens (P)
P = 1/f
f must be in meters. Unit is Dioptre (D). P is +ve for converging, -ve for diverging.
Combination of Lenses
1/F_eq = 1/f₁ + 1/f₂
P_eq = P₁ + P₂
P_eq = P₁ + P₂
For thin lenses in contact. Use with proper signs.
BITSAT Speed Hacks
Sign Convention is KING. Always use the Cartesian sign convention (origin at optical center/pole).
For a silvered lens, treat it as a combination of lens-mirror-lens. P_total = 2P_lens + P_mirror.
If a lens is cut horizontally, focal length remains 'f'. If cut vertically, it becomes '2f'.
In YDSE, if a thin film (thickness t, refractive index μ) is introduced, the fringe shift is Δy = (μ-1)tD/d.
Remember β ∝ λ. Red light (longer λ) gives wider fringes than violet light (shorter λ).
For telescopes, a large objective aperture improves resolving power (θ = 1.22λ/D) and light gathering ability.
Wave Optics: Interference & Diffraction
YDSE: Path Difference (Δx)
Δx = d sinθ ≈ d y / D
d = slit separation, D = screen distance, y = position on screen.
YDSE: Fringe Conditions
Maxima: Δx = nλ
Minima: Δx = (2n-1)λ/2
Minima: Δx = (2n-1)λ/2
n = 0, 1, 2... for maxima. n = 1, 2, 3... for minima.
YDSE: Fringe Width (β)
β = λD / d
Distance between two consecutive bright or dark fringes. Independent of 'n'.
Single Slit Diffraction (Minima)
a sinθ = nλ
Condition for the nth dark fringe. 'a' is the slit width. n = 1, 2, 3...
Width of Central Maximum
W = 2λD / a
It is twice the width of other secondary maxima (which are λD/a).
Polarization & EM Waves
Malus's Law
I = I₀ cos²θ
Intensity (I) of polarized light after passing through an analyzer. θ is the angle between polarizer and analyzer axes.
Brewster's Law
n = tan θp
At Brewster's angle (θp), the reflected light is completely plane-polarized. Reflected and refracted rays are ⊥.
EM Wave Properties
E & B are ⊥ to each other and to direction of propagation.
c = E₀ / B₀
c = E₀ / B₀
Qualitative concept. Remember the order of the EM spectrum (Raging Martians Invaded Venus Using X-ray Guns).
Optical Instruments at a Glance
| Feature | Compound Microscope | Astronomical Telescope |
|---|---|---|
Objective Lens | Small focal length (f₀), small aperture | Large focal length (f₀), large aperture |
Eyepiece Lens | Small focal length (fₑ) | Small focal length (fₑ) |
Magnifying Power (Normal Adj.) | M ≈ (L/f₀) × (D/fₑ) | M = f₀/fₑ |
Tube Length (Normal Adj.) | L ≈ v₀ + fₑ | L = f₀ + fₑ |
Final Image | Virtual, inverted, highly magnified | Virtual, inverted, magnified |