Wave Optics — MHT-CET Physics

Formulas (2)

• Wavefronts and the Wave Theory · Wavelength in a medium
  $$\lambda_{\text{medium}} = \frac{\lambda_{\text{vacuum}}}{\mu}, \qquad N = \frac{\mu t}{\lambda}$$
• Coherent Sources · Condition for a steady pattern
  $$\nu_1 = \nu_2, \quad \phi_1 - \phi_2 = \text{constant}$$

Watch out for (2)

• Crediting Huygens with corpuscles
  → Wavefronts and the Wave Theory
• Expecting red and blue fringes side by side
  → Coherent Sources

Formulas (3)

• Fringe Width · Fringe width
  $$\beta = \frac{\lambda D}{d}$$
• Positions of Bright and Dark Fringes · Fringe positions
  $$y_{\text{bright}} = n\beta, \qquad y_{\text{dark}} = \left(n - \tfrac{1}{2}\right)\beta$$
• A Transparent Sheet Over One Slit · Fringe shift
  $$\Delta y = \frac{(\mu - 1)tD}{d}, \qquad N = \frac{(\mu - 1)t}{\lambda}$$

Watch out for (3)

• Multiplying the medium's μ
  → Fringe Width
• Placing the nth dark fringe at nβ
  → Positions of Bright and Dark Fringes
• Using μt instead of (μ − 1)t
  → A Transparent Sheet Over One Slit

Formulas (2)

• Intensity From the Phase Difference · Two equal coherent sources
  $$I = 4I_0\cos^2\frac{\phi}{2}, \qquad \phi = \frac{2\pi}{\lambda}\,\Delta x$$
• Unequal Sources: Maxima, Minima and Contrast · Maxima and minima
  $$\frac{I_{\max}}{I_{\min}} = \left(\frac{\sqrt{I_1} + \sqrt{I_2}}{\sqrt{I_1} - \sqrt{I_2}}\right)^2$$

Watch out for (2)

• Forgetting to halve the phase
  → Intensity From the Phase Difference
• Taking the intensity ratio as the max–min ratio
  → Unequal Sources: Maxima, Minima and Contrast

Formulas (3)

• Minima and the Central Maximum · Single-slit minima
  $$a\sin\theta = n\lambda, \qquad W_{\text{central}} = \frac{2\lambda D}{a}$$
• Secondary Maxima · Secondary maxima
  $$a\sin\theta = \left(n + \tfrac{1}{2}\right)\lambda$$
• Resolving Power · Angular resolution
  $$\Delta\theta = \frac{1.22\lambda}{D}$$

Watch out for (3)

• Half-width or full width
  → Minima and the Central Maximum
• Using nλ for a maximum
  → Secondary Maxima
• A longer wavelength sees finer detail
  → Resolving Power

Formulas (2)

• Malus' Law and Chains of Polaroids · Malus' law
  $$I = I_{\text{in}}\cos^2\theta$$
• Brewster's Angle · Brewster's law
  $$\tan i_p = \mu = \frac{c}{v}$$

Watch out for (2)

• Measuring every angle from the first polaroid
  → Malus' Law and Chains of Polaroids
• Using sin instead of tan
  → Brewster's Angle