PiTheory

Wave Optics formulas

Class 12 physics formula sheet for NEET and JEE: the key equations of NCERT chapter 10, the special cases questions are built on, and diagrams where they help.

29 formulas5 sectionsClass 12 · Chapter 102 of 5 sections free

By Sreeraj P, M.Sc Physics · 10+ years teaching NEET and JEE

Most used formulasOther formulas and cases

1Wavefronts and Huygens

  • Wavefront: locus of points in the same phase; rays are normal to it. Point source → spherical ($I\propto1/r^2$, $A\propto1/r$); line source → cylindrical ($I\propto1/r$, $A\propto1/\sqrt r$); distant source → plane.
  • Huygens: each point on a wavefront sends forward secondary wavelets; their envelope is the new wavefront. Gives the laws of reflection and refraction $\left(\dfrac{\sin i}{\sin r}=\dfrac{v_1}{v_2}\right)$. Convex lens turns a plane wavefront into a converging spherical one; prism tilts it.
$$\frac{\text{width of refracted beam}}{\text{width of incident beam}}=\frac{\cos r}{\cos i}$$
$$\frac{\Delta\lambda}{\lambda}=-\frac{\Delta f}{f}=\frac{v}{c}\quad(v\ll c,\ \text{receding})$$
$$\begin{array}{l}\displaystyle \frac{\Delta\lambda}{\lambda}=-\frac{\Delta f}{f}=\frac{v}{c}\\[6pt]\displaystyle (v\ll c,\ \text{receding})\end{array}$$

Doppler effect for light: receding → red shift ($\lambda$ increases); approaching → blue shift.

2Superposition and interference

$$A^2=A_1^2+A_2^2+2A_1A_2\cos\phi,\qquad I=I_1+I_2+2\sqrt{I_1I_2}\cos\phi$$
$$\begin{array}{l}\displaystyle A^2=A_1^2+A_2^2+2A_1A_2\cos\phi\\[6pt]\displaystyle I=I_1+I_2+2\sqrt{I_1I_2}\cos\phi\end{array}$$

Coherent sources (constant phase difference; derived from one source). Incoherent: $I=I_1+I_2$ (cos averages to zero); $n$ incoherent sources: $nI_0$, coherent in phase: $n^2I_0$.

$$\phi=\frac{2\pi}{\lambda}\Delta x,\qquad \text{bright: }\Delta x=n\lambda,\qquad \text{dark: }\Delta x=\left(n-\tfrac12\right)\lambda$$
$$\begin{array}{l}\displaystyle \phi=\frac{2\pi}{\lambda}\Delta x\\[6pt]\displaystyle \text{bright: }\Delta x=n\lambda\\[6pt]\displaystyle \text{dark: }\Delta x=\left(n-\tfrac12\right)\lambda\end{array}$$

Constructive: $\phi=2n\pi$; destructive: $\phi=(2n-1)\pi$.

$$\begin{array}{l}\displaystyle \frac{I_{\max}}{I_{\min}}=\left(\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right)^2=\left(\frac{A_1+A_2}{A_1-A_2}\right)^2\\[5pt]\displaystyle V=\frac{I_{\max}-I_{\min}}{I_{\max}+I_{\min}}=\frac{2\sqrt{I_1I_2}}{I_1+I_2}\end{array}$$

Given $I_{\max}/I_{\min}=r$: $\dfrac{A_1}{A_2}=\dfrac{\sqrt r+1}{\sqrt r-1}$. Equal intensities: $I=4I_0\cos^2\dfrac\phi2$, $I_{\min}=0$, $V=1$. Energy is only redistributed.

3 more sections and 20 formulas in the full chapter

  1. 3Young's double slit8 formulas · 1 case table · 1 diagram
  2. 4Diffraction8 formulas · 1 case table · 1 diagram
  3. 5Polarisation4 formulas · 1 diagram

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