Optics formulas for JEE Main & Advanced

20 formula entries for Optics, in the order the chapter builds them. Each shows the formula, when to use it and the first trap to avoid.

Refraction of Light

n_{1} \sin i = n_{2} \sin r

When to use. Use for any problem involving light crossing a boundary between two media.

Trap. Using degrees in sin calculations without converting to radians when needed; always use degrees in JEE.

Critical Angle and Total Internal Reflection (TIR)

\sin C = \frac{n_{2}}{n_{1}}

where

n_{1} > n_{2}

When to use. Use in problems involving optical fibers, mirages, or diamond sparkle.

Trap. Applying TIR when light goes from rarer to denser; it only occurs from denser to rarer.

Mirror Formula

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

When to use. Use to find image position or focal length in mirror problems.

Trap. Sign convention errors: use Cartesian sign convention (distances measured from pole, positive in direction of incident light).

Magnification for Mirrors

m = \frac{h_{i}}{h_{o}} = - \frac{v}{u}

When to use. Use to find image size or orientation in mirror problems.

Trap. Forgetting the negative sign: it indicates image orientation (inverted if negative).

Lens Formula

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

When to use. Use for any thin lens problem involving image formation.

Trap. Sign convention: for convex lens, $f$ is positive; for concave, $f$ is negative. $u$ is negative for real objects.

Lens Maker's Formula

\frac{1}{f} = (n - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})

When to use. Use to find focal length of a lens given its geometry and material.

Trap. Sign convention for $R_{1}$ and $R_{2}$ : positive if center of curvature is on the outgoing side.

Magnification for Lenses

m = \frac{h_{i}}{h_{o}} = \frac{v}{u}

When to use. Use to find image size or orientation in lens problems.

Trap. No negative sign here (unlike mirrors); sign of $m$ comes from $v$ and $u$ signs.

Power of a Lens

P = \frac{1}{f}

(in meters), unit: diopter (D)

When to use. Use in problems involving lens combinations or optometry.

Trap. Using $f$ in cm; always convert to meters for power in diopters.

Combination of Lenses (in contact)

P_{n e t} = P_{1} + P_{2} + P_{3} + . . .

When to use. Use when multiple lenses are placed close together.

Trap. Forgetting sign of each lens's power.

Prism and Angle of Deviation

δ = i + e - A

(for small angles,

δ = (n - 1) A

)

When to use. Use in problems involving prism geometry and dispersion.

Trap. Using the formula $δ = (n - 1) A$ only for thin prisms (small $A$ ).

Refractive Index from Prism (Minimum Deviation)

n = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin (\frac{A}{2})}

When to use. Use to find refractive index of prism material from experimental data.

Trap. Using this formula when deviation is not minimum; it's only valid at $δ_{m}$ .

Dispersion of Light

Angular dispersion =

δ_{v} - δ_{r}

When to use. Use in problems involving rainbows, prisms, or chromatic aberration.

Trap. Assuming all colors deviate equally; violet deviates most, red least.

Dispersive Power

ω = \frac{δ_{v} - δ_{r}}{δ_{y}}

where

δ_{y}

is deviation for yellow light

When to use. Use to compare dispersive properties of different materials.

Trap. Using wavelengths instead of deviations in the formula.

Optical Instruments: Simple Microscope

Magnifying power

M = 1 + \frac{D}{f}

(for final image at near point

D = 25

cm)

When to use. Use in problems on simple magnifiers.

Trap. Using $M = D / f$ for relaxed eye (image at infinity); that's a different formula.

Compound Microscope

Total magnification

M = m_{o} \times m_{e} = (- \frac{L}{f_{o}}) \times (1 + \frac{D}{f_{e}})

(near point)

When to use. Use in problems on compound microscopes.

Trap. Forgetting the negative sign for objective magnification (inverted image).

Astronomical Telescope

Magnifying power

M = - \frac{f_{o}}{f_{e}}

(for relaxed eye, image at infinity)

When to use. Use in problems on astronomical telescopes.

Trap. Forgetting the negative sign indicates inverted image.

Interference of Light

Path difference

Δ x = n λ

for maxima,

(2 n + 1) λ / 2

for minima

When to use. Use in Young's double-slit experiment or thin film problems.

Trap. Forgetting that sources must be coherent (constant phase difference).

Young's Double-Slit Experiment (YDSE)

Fringe width

β = \frac{λ D}{d}

When to use. Use to find fringe spacing or wavelength in YDSE.

Trap. Using $d$ as slit width (it's slit separation); slit width affects diffraction, not interference.

Diffraction of Light

For single slit: minima at

a \sin θ = n λ

When to use. Use in problems on single-slit diffraction or resolving power.

Trap. Confusing diffraction with interference: diffraction pattern has a central maximum twice as wide.

Resolving Power of Optical Instruments

For telescope:

θ_{m i n} = 1.22 \frac{λ}{D}

; For microscope:

d_{m i n} = \frac{1.22 λ}{2 \sin θ}

When to use. Use in problems on telescopes, microscopes, or human eye resolution.

Trap. Using $D$ as diameter of objective, not magnification.

Values to remember

$n_{a i r} \approx 1$ Refraction of Light
$n_{w a t e r} \approx 4 / 3$ Refraction of Light
$n_{g l a s s} \approx 3 / 2$ Refraction of Light
$C_{w a t e r - a i r} \approx {48.6}^{\circ}$ Critical Angle and Total Internal Reflection (TIR)
$C_{g l a s s - a i r} \approx {41.8}^{\circ}$ Critical Angle and Total Internal Reflection (TIR)
$D = 25$ cm Optical Instruments: Simple Microscope

Read the full chapter: Optics for JEE, with what JEE asks and the common traps.