Optics (Ray Optics & Wave Optics) - Important Formulas Table

 Optics (Ray Optics & Wave Optics) - Important Formulas Table

S.No.	Concept / Quantity	Formula	Key Notes
1	Mirror Formula	$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$	Sign convention: New Cartesian
2	Magnification (Mirror)	$m = -\frac{v}{u} = \frac{h_i}{h_o}$	Lateral magnification
3	Lens Formula	$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$	Thin lens
4	Lens Maker’s Formula	$\frac{1}{f} = (n-1)\left( \frac{1}{R_1} - \frac{1}{R_2} \right)$	For thin lens in air
5	Magnification (Lens)	$m = \frac{v}{u} = \frac{h_i}{h_o}$	-
6	Power of Lens	$P = \frac{1}{f}$ (f in metre)	Unit: Dioptre (D)
7	Equivalent Focal Length (Two thin lenses)	$\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2} - \frac{d}{f_1 f_2}$	d = separation
8	Refraction at Single Surface	$\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R}$	-
9	Snell’s Law	$n_1 \sin i = n_2 \sin r$	-
10	Critical Angle	$\sin C = \frac{1}{\mu}$	For denser to rarer
11	Total Internal Reflection (TIR)	Occurs when $i > C$	Optical fibre principle
12	Lateral Shift in Glass Slab	$d = t \sin i \left(1 - \frac{1}{\mu}\right)$	t = thickness
13	Prism Deviation	$\delta = i + e - A$	Minimum deviation $\delta_m = 2i - A$
14	Prism Refractive Index (Minimum Deviation)	$\mu = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin(A/2)}$	-
15	Apparent Depth	$d' = \frac{d}{\mu}$	For small angles
16	Combination of Prism (Dispersion without Deviation)	$\delta_1 + \delta_2 = 0$	Crown + Flint glass
17	Young’s Double Slit – Path Difference	$\Delta x = d \sin\theta$	-
18	Condition for Bright Fringe	$d \sin\theta = m\lambda$ (m = 0,1,2…)	Constructive interference
19	Condition for Dark Fringe	$d \sin\theta = (2m+1)\frac{\lambda}{2}$	Destructive interference
20	Fringe Width	$\beta = \frac{\lambda D}{d}$	D = distance to screen
21	Intensity in Interference	$I = 4I_0 \cos^2(\phi/2)$	$\phi$ = phase difference
22	Single Slit Diffraction – Minima	$a \sin\theta = m\lambda$ (m=1,2,3…)	Central maxima width = $\frac{2\lambda D}{a}$
23	Resolving Power of Microscope	$RP = \frac{1}{d_{\min}} = \frac{2\mu \sin\theta}{\lambda}$	-
24	Resolving Power of Telescope	$RP = \frac{D}{1.22\lambda}$	D = diameter of objective
25	Polarisation by Reflection (Brewster’s Law)	$\tan i_B = \mu$	$i_B$ = polarizing angle
26	Malus Law	$I = I_0 \cos^2\theta$	Intensity after polarizer
27	Optical Path Length	$\text{OPL} = \mu \times \text{geometrical path}$	-
28	Condition for Constructive Reflection (Thin Film)	$2\mu t \cos r = (m + \frac{1}{2})\lambda$ (reflection)	Phase change consideration
29	Doppler Shift in Light	$\frac{\Delta\lambda}{\lambda} = \frac{v}{c}$	For v << c
30	Rayleigh Criterion for Resolution	$\theta = 1.22 \frac{\lambda}{D}$	Limit of resolution

Important Constants & Relations

• Speed of light in vacuum: $c = 3 \times 10^8$ m/s
• Refractive index of glass ≈ 1.5, water ≈ 1.33
• $\mu = \frac{\sin i}{\sin r}$

Note: All formulas are in SI units. This table covers the complete Optics chapter (Ray Optics + Wave Optics) for Class 12 Board Exams, JEE Main, JEE Advanced, and NEET.