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

Question

You need a single-page revision sheet covering all major optics formulas — mirrors, lenses, prisms, and wave optics. Which formulas should you prioritise, and how do they connect?

(Frequently tested across JEE Main, NEET, and CBSE Class 12 boards)

Solution — Step by Step

The mirror formula applies to both concave and convex mirrors:

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

Magnification: $m = -\dfrac{v}{u}$

Sign convention matters here — we use the New Cartesian Sign Convention where distances measured against the incident light are negative.

For thin lenses:

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

Notice the minus sign — that is the difference from the mirror formula. Power of a lens: $P = \dfrac{1}{f}$ (in metres, gives dioptres).

Lens maker’s equation: $\dfrac{1}{f} = (\mu - 1)\left(\dfrac{1}{R_1} - \dfrac{1}{R_2}\right)$

Deviation by a prism: $\delta = (i_1 + i_2) - A$ , where $A$ is the prism angle.

At minimum deviation: $i_1 = i_2$ and $r_1 = r_2 = A/2$

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

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

Young’s double slit: fringe width $\beta = \dfrac{\lambda D}{d}$

Single slit diffraction: first minimum at $a \sin\theta = \lambda$

Brewster’s angle: $\tan i_B = \mu$

Malus’s law: $I = I_0 \cos^2\theta$

graph TD
    A[Optics Problem] --> B{Ray or Wave?}
    B -->|Ray Optics| C{Mirror or Lens?}
    B -->|Wave Optics| D{Interference or Diffraction?}
    C -->|Mirror| E["1/v + 1/u = 1/f"]
    C -->|Lens| F["1/v - 1/u = 1/f"]
    C -->|Prism| G["delta = i1 + i2 - A"]
    D -->|YDSE| H["beta = lambda D / d"]
    D -->|Single Slit| I["a sin theta = n lambda"]
    D -->|Polarisation| J["I = I0 cos2 theta"]
    E --> K[Sign Convention Check]
    F --> K

Why This Works

Optics formulas follow a logical chain. Mirrors and lenses share the same physics — image formation by reflection or refraction — so their formulas look similar with a sign difference. Prism formulas connect refraction at two surfaces. Wave optics adds the interference and diffraction layer.

The decision tree above is your exam strategy: first identify whether the problem is ray or wave optics, then pick the right sub-formula. Most marks are lost not because students don’t know the formula, but because they apply the wrong sign convention or confuse which formula applies.

Alternative Method

For combination of lenses in contact, use $P_{total} = P_1 + P_2$ . This is faster than finding individual focal lengths and combining them. JEE Main loves asking about lens combinations — the power addition approach saves a good minute per problem.

For mirror problems, you can also use the u-v graphical method: plot $1/v$ vs $1/u$ . The intercepts on both axes give $1/f$ . This helps when you need to verify your sign convention is correct.

Common Mistake

The single biggest error in optics: mixing up the mirror formula ( $1/v + 1/u = 1/f$ ) with the lens formula ( $1/v - 1/u = 1/f$ ). Students memorise one and apply it everywhere.

The physical reason for the difference: in mirrors, object and image are on the same side of the reflecting surface. In lenses, they are on opposite sides. This changes the sign relationship between $u$ and $v$ .

Always write down which formula you are using before substituting numbers.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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