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Wave Optics formulas

Master Wave Optics through 30 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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Wave Optics, every formula

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Resultant intensity
$I = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ$
Q1MCQResultant intensity
The resultant intensity of two coherent waves is:
- A
  $I_1+I_2+2\sqrt{I_1 I_2}\cos\phi$
- B
  $I_1+I_2$
- C
  $I_1 I_2$
- D
  $\sqrt{I_1 I_2}$
Maximum intensity
$I_{m a x} = (I_{1} + I_{2})^{2}$
Q1MCQMax intensity
The maximum interference intensity is:
- A
  $(\sqrt{I_1}+\sqrt{I_2})^{2}$
- B
  $I_1+I_2$
- C
  $(\sqrt{I_1}-\sqrt{I_2})^{2}$
- D
  $2\sqrt{I_1 I_2}$
Minimum intensity
$I_{m i n} = (I_{1} - I_{2})^{2}$
Q1MCQMin intensity
The minimum interference intensity is:
- A
  $(\sqrt{I_1}-\sqrt{I_2})^{2}$
- B
  $(\sqrt{I_1}+\sqrt{I_2})^{2}$
- C
  $0$ always
- D
  $I_1+I_2$
Intensity for equal sources
$I = 4 I_{0} cos^{2} (\frac{ϕ}{2})$
Q1MCQEqual sources
For two equal coherent sources, the intensity is:
- A
  $4I_0\cos^{2}\!\left(\dfrac{\phi}{2}\right)$
- B
  $2I_0$
- C
  $I_0\cos\phi$
- D
  $4I_0$
Incoherent sources
$I = I_{1} + I_{2}$
Q1MCQIncoherent
For incoherent sources, the resultant intensity is:
- A
  $I_1+I_2$
- B
  $I_1+I_2+2\sqrt{I_1 I_2}$
- C
  $(\sqrt{I_1}+\sqrt{I_2})^{2}$
- D
  $0$
Amplitude ratio
$\frac{a _{1}}{a _{2}} = \frac{I _{1}}{I _{2}}$
Q1MCQAmplitude ratio
The amplitude ratio in terms of intensities is:
- A
  $\sqrt{\dfrac{I_1}{I_2}}$
- B
  $\dfrac{I_1}{I_2}$
- C
  $\dfrac{I_1^{2}}{I_2^{2}}$
- D
  $I_1 I_2$
YDSE path difference
$Δ p = d sin θ = \frac{d y}{D}$
Q1MCQPath difference
The path difference in YDSE is:
- A
  $\dfrac{dy}{D}$
- B
  $\dfrac{Dy}{d}$
- C
  $dD$
- D
  $\dfrac{d}{y}$
Bright fringe position
$y_{n} = \frac{nλ D}{d}$
Q1MCQBright fringe
The position of the $n$th bright fringe is:
- A
  $\dfrac{n\lambda D}{d}$
- B
  $\dfrac{(2n-1)\lambda D}{2d}$
- C
  $\dfrac{\lambda D}{d}$
- D
  $n\lambda$
Dark fringe position
$y_{n} = \frac{( 2 n - 1 ) λ D}{2 d}$
Q1MCQDark fringe
The position of the $n$th dark fringe is:
- A
  $\dfrac{(2n-1)\lambda D}{2d}$
- B
  $\dfrac{n\lambda D}{d}$
- C
  $\dfrac{\lambda D}{d}$
- D
  $\dfrac{n\lambda D}{2d}$
Fringe width
$β = \frac{λ D}{d}$
Phase difference
$Δ ϕ = \frac{2 π}{λ} Δ p$
Q1MCQPhase difference
The phase difference for path difference $\Delta p$ is:
- A
  $\dfrac{2\pi}{\lambda}\Delta p$
- B
  $\dfrac{\lambda}{2\pi}\Delta p$
- C
  $\pi\Delta p$
- D
  $\dfrac{\Delta p}{\lambda}$
Highest-order maxima
$n_{m a x} = ⌊ \frac{d}{λ} ⌋$
Q1MCQHighest order
The highest order of maxima in YDSE is about:
- A
  $\dfrac{d}{\lambda}$
- B
  $\dfrac{\lambda}{d}$
- C
  $d\lambda$
- D
  $\dfrac{D}{\lambda}$
Fringe shift due to a slab
$Δ x = \frac{D}{d} (μ - 1) t$
Q1MCQFringe shift
Introducing a slab of thickness $t$ shifts the fringe pattern by:
- A
  $\dfrac{D}{d}(\mu-1)t$
- B
  $\dfrac{D}{d}\mu t$
- C
  $(\mu-1)t$
- D
  $\dfrac{d}{D}(\mu-1)t$
Thin film (reflected) maxima
$2 μ t cos r = (2 n - 1) \frac{λ}{2}$
Q1MCQThin film maxima
For constructive interference in a reflected thin film:
- A
  $2\mu t\cos r=(2n-1)\dfrac{\lambda}{2}$
- B
  $2\mu t\cos r=n\lambda$
- C
  $\mu t=n\lambda$
- D
  $2\mu t=n\lambda$
Thin film (reflected) minima
$2 μ t cos r = nλ$
Q1MCQThin film minima
For destructive interference in a reflected thin film:
- A
  $2\mu t\cos r=n\lambda$
- B
  $2\mu t\cos r=(2n-1)\dfrac{\lambda}{2}$
- C
  $\mu t=n\lambda$
- D
  $2\mu t=\lambda$
Thin film (transmitted) maxima
$2 μ t cos r = nλ$
Q1MCQTransmitted maxima
For constructive interference in transmitted light:
- A
  $2\mu t\cos r=n\lambda$
- B
  $2\mu t\cos r=(2n-1)\dfrac{\lambda}{2}$
- C
  $\mu t=n\lambda$
- D
  $2\mu t=\lambda$
Single-slit minima
$a sin θ = nλ$
Q1MCQSingle-slit minima
The minima of a single-slit pattern occur at:
- A
  $a\sin\theta=n\lambda$
- B
  $a\sin\theta=(2n+1)\dfrac{\lambda}{2}$
- C
  $d\sin\theta=n\lambda$
- D
  $a\sin\theta=\dfrac{\lambda}{2}$
Single-slit secondary maxima
$a sin θ = (2 n + 1) \frac{λ}{2}$
Q1MCQSingle-slit maxima
The secondary maxima of single-slit diffraction occur at:
- A
  $a\sin\theta=(2n+1)\dfrac{\lambda}{2}$
- B
  $a\sin\theta=n\lambda$
- C
  $d\sin\theta=n\lambda$
- D
  $a\sin\theta=\lambda$
Angular width of central maximum
$W_{θ} = \frac{2 λ}{a}$
Q1MCQAngular width
The angular width of the central diffraction maximum is:
- A
  $\dfrac{2\lambda}{a}$
- B
  $\dfrac{\lambda}{a}$
- C
  $\dfrac{2a}{\lambda}$
- D
  $\dfrac{\lambda}{2a}$
Linear width of central maximum
$W = \frac{2 D λ}{a}$
Q1MCQLinear width
The linear width of the central maximum on a screen at distance $D$ is:
- A
  $\dfrac{2D\lambda}{a}$
- B
  $\dfrac{D\lambda}{a}$
- C
  $\dfrac{2\lambda}{a}$
- D
  $\dfrac{2Da}{\lambda}$
Single-slit intensity
$I = I_{0} (\frac{sin ( β /2 )}{β /2})^{2}$
Q1MCQSingle-slit intensity
The single-slit intensity pattern is:
- A
  $I_0\left(\dfrac{\sin(\beta/2)}{\beta/2}\right)^{2}$
- B
  $I_0\cos^{2}\beta$
- C
  $I_0\sin\beta$
- D
  $I_0$
Malus's law
$I = I_{0} cos^{2} θ$
Q1MCQMalus's law
The intensity of polarized light through an analyser at angle $\theta$ is:
- A
  $I_0\cos^{2}\theta$
- B
  $I_0\sin^{2}\theta$
- C
  $I_0\cos\theta$
- D
  $\dfrac{I_0}{2}$
Brewster's law
$μ = tan i_{p}$
Q1MCQBrewster's law
Brewster's law states:
- A
  $\mu=\tan i_p$
- B
  $\mu=\sin i_p$
- C
  $\mu=\cos i_p$
- D
  $\mu=i_p$
Brewster angle relation
$i_{p} + r_{p} = 9 0^{\circ}$
Q1MCQBrewster relation
At the polarizing angle, the reflected and refracted rays are:
- A
  perpendicular ($i_p+r_p=90^{\circ}$)
- B
  parallel
- C
  antiparallel
- D
  at $45^{\circ}$
Optical activity
$[α] = \frac{θ}{L C}$
Q1MCQOptical activity
The specific rotation of an optically active solution is:
- A
  $\dfrac{\theta}{L\,C}$
- B
  $\theta L C$
- C
  $\dfrac{L C}{\theta}$
- D
  $\theta$
Resolving power (grating)
$R = \frac{λ}{Δ λ}$
Q1MCQResolving power
The resolving power of a grating is:
- A
  $\dfrac{\lambda}{\Delta\lambda}$
- B
  $\dfrac{\Delta\lambda}{\lambda}$
- C
  $\lambda\Delta\lambda$
- D
  $\dfrac{1}{\lambda}$
Optical path difference
$Δ_{o pt} = μ Δ p$
Q1MCQOptical path
The optical path difference is:
- A
  $\mu\,\Delta p$
- B
  $\dfrac{\Delta p}{\mu}$
- C
  $\Delta p$
- D
  $\mu+\Delta p$
Two-wavelength coincidence
$n_{1} β_{1} = n_{2} β_{2}$
Q1MCQTwo-wavelength coincidence
Bright fringes of two wavelengths coincide when:
- A
  $n_1\beta_1=n_2\beta_2$
- B
  $\beta_1=\beta_2$
- C
  $n_1=n_2$
- D
  $\lambda_1=\lambda_2$
EM wave amplitude relation
$E_{0} = B_{0} c$
Q1MCQEM amplitude
For an EM wave, the field amplitudes satisfy:
- A
  $E_0=B_0 c$
- B
  $B_0=E_0 c$
- C
  $E_0=B_0$
- D
  $E_0 B_0=c$
Speed of EM waves in a medium
$v = \frac{1}{μ ε}$
Q1MCQEM speed
The speed of EM waves in a medium is:
- A
  $\dfrac{1}{\sqrt{\mu\varepsilon}}$
- B
  $\sqrt{\mu\varepsilon}$
- C
  $\dfrac{1}{\mu\varepsilon}$
- D
  $\mu\varepsilon$

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Wave Optics formulas

Wave Optics, every formula

Resultant intensity

Maximum intensity

Minimum intensity

Intensity for equal sources

Incoherent sources

Amplitude ratio

YDSE path difference

Bright fringe position

Dark fringe position

Fringe width

Phase difference

Highest-order maxima

Fringe shift due to a slab

Thin film (reflected) maxima

Thin film (reflected) minima

Thin film (transmitted) maxima

Single-slit minima

Single-slit secondary maxima

Angular width of central maximum

Linear width of central maximum

Single-slit intensity

Malus's law

Brewster's law

Brewster angle relation

Optical activity

Resolving power (grating)

Optical path difference

Two-wavelength coincidence

EM wave amplitude relation

Speed of EM waves in a medium

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