Wave optics Formulas- Physics Formulas
Wave Optics Formulas
1. Constructive Interference
Resultant Amplitude
`a_R=a_1+a_2`
Phase Difference
`theta`= 0, 2π, 4π,.....(2nπ)
where n=0, 1, 2, 3, 4,.....
Path Difference
x= 0, `\lambda,2\lambda,3\lambda,.......n\lambda`
Where n=0, 1, 2, 3,....
Resultant Intensity
`I_{max}=\left(a_1+a_2\right)^2\=\(\sqrt{I_1}+\sqrt{I_2})^2`
`I_{max}=I_1+I_2+2\sqrt{I_1I_2}`
2. Destructive Interference
Resultant Amplitude
`a_R=a_1-a_2`
Phase difference
`theta`=π, 3π, 5π,......(2n-1) π
where n=1, 2,3,......
Path difference
`x=\frac\lambda2,\frac{2\lambda}2,\.......(2n-1)\frac\lambda2`
Resultant Intensity
`I_{min}=(a_1-a_2)^2=(\sqrt{I_1}-\sqrt{I_2})^2`
3. When sources are coherent
`\frac{I_{max}}{I_{min}}=\frac{{(a+b)}^2}{{(a-b)}^2}=\frac{{(\sqrt{I_1}+\sqrt{I_2}\)}^2}{{(\sqrt{I_1}-\sqrt{I_2})}^2}`
4. Young's Double slit experiment
Bright Fringe
`x=n\frac{\lambda D}d`
Dark Fringe
`x=\left(\frac{2n-1}2\right)\frac{\lambda D}d`
Fringe width
`\beta=\frac{\lambda D}d`
5. Single slit experiment
Angular Position of nth secondary minima
`\theta_n=\frac{n\lambda}a`
Angular Position of nth secondary maxima
`(\theta^')_n=\frac{(2n-1)\lambda}{2a}`
Angular width of central maxima
`\theta_c=\frac{2\lambda}a`
Angular width of secondary maximum and minimum
`\theta=\frac\lambda a`
6. Brewster's Law
`\mu=\tan i_p`
7. Law of Malus
`I=I_0\cos^2\theta`
8. Resolving power of telescope
`R.P.=\frac1{d\theta}=\frac D{1.22\lambda}`