Optics formula sheet — mirror, lens, prism, wave optics in one page

Question

Compile all the essential optics formulas — mirrors, lenses, prism, and wave optics — in one place. For each formula, state when to use it.

(JEE Main + NEET + CBSE 12 revision)

Solution — Step by Step

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

When to use: Any problem involving concave or convex mirrors. Sign convention: distances measured from pole, towards incident light is negative.

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

When to use: Any problem involving convex or concave lenses. Note the minus sign — different from mirror formula.

Magnification: Mirror: $m = -\frac{v}{u}$ , Lens: $m = \frac{v}{u}$

Power of lens: $P = \frac{1}{f(\text{in metres})}$ (unit: dioptre)

\delta = (i_1 + i_2) - A

At minimum deviation ( $\delta_m$ ):

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

When to use: When given prism angle $A$ , angles of incidence/emergence, or minimum deviation.

For thin prism: $\delta = (\mu - 1)A$

Fringe width: $\beta = \frac{\lambda D}{d}$

Position of $n$ -th bright fringe: $y_n = \frac{n\lambda D}{d}$

Position of $n$ -th dark fringe: $y_n = \frac{(2n-1)\lambda D}{2d}$

First minimum: $a\sin\theta = \lambda$

Central maximum width: $\frac{2\lambda D}{a}$ (twice the fringe width)

When to use YDSE: Two slits, interference pattern. When to use single slit: One slit, diffraction pattern.

Optics Problem Type Decision Tree

flowchart TD
    A["Optics problem"] --> B{"Type?"}
    B -->|"Mirror"| C["1/v + 1/u = 1/f"]
    B -->|"Lens"| D["1/v - 1/u = 1/f"]
    B -->|"Prism"| E["δ = i₁ + i₂ - A"]
    B -->|"Interference"| F["β = λD/d"]
    B -->|"Diffraction"| G["a sin θ = nλ"]
    C --> H{"Concave or convex?"}
    H -->|"Concave"| I["f is negative"]
    H -->|"Convex"| J["f is positive"]
    D --> K{"Converging or diverging?"}
    K -->|"Convex lens"| L["f is positive"]
    K -->|"Concave lens"| M["f is negative"]

Why This Works

Optics problems are formula-driven — once you identify the device (mirror, lens, prism, slit), the formula is almost automatic. The real challenge is sign convention and substitution.

For JEE and NEET, roughly 3-4 questions per paper come from optics. YDSE fringe width problems are the most common wave optics question — they appeared in JEE Main 2023 and 2024 both.

Common Mistake

The most common error in optics: mixing up sign conventions. The mirror formula has $\frac{1}{v} + \frac{1}{u}$ , while the lens formula has $\frac{1}{v} - \frac{1}{u}$ . Also, for mirrors, magnification is $-v/u$ (note the negative), while for lenses it is $v/u$ (no negative). Write the formula first, then substitute with signs — never do signs in your head.

For YDSE problems, always check whether the question asks for bright or dark fringes. Bright: $y = n\lambda D/d$ . Dark: $y = (2n-1)\lambda D/2d$ . The factor of $(2n-1)/2$ for dark fringes is where marks are lost.

Question

Solution — Step by Step

Optics Problem Type Decision Tree

Why This Works

Common Mistake

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