Optics — Applied Wave Optics (Medium)

Quick Recap — Wave Optics in Action

• YDSE: fringe width $\beta=\dfrac{\lambda D}{d}$; $n$-th bright at $y_n=n\beta$; in a medium $\beta\to\beta/n$.
• Thin sheet over one slit: shift $=\dfrac{(n-1)tD}{d}$, i.e. $N=\dfrac{(n-1)t}{\lambda}$ fringes.
• Single slit: first minimum $a\sin\theta=\lambda$; central maximum width $=\dfrac{2\lambda D}{a}$, angular width $\dfrac{2\lambda}{a}$.
• Polarisation: Malus $I=I_0\cos^2\theta$; unpolarised loses half at the first Polaroid; Brewster $\tan\theta_B=n$.
• Two sources: $\dfrac{I_{max}}{I_{min}}=\left(\dfrac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right)^2$; and $I=I_{max}\cos^2\!\dfrac{\phi}{2}$ with $\phi=\dfrac{2\pi}{\lambda}\Delta x$.

Worked mini-example. $\lambda=600$ nm, $D=1.5$ m, $d=0.5$ mm: $\beta=\dfrac{(600\times10^{-9})(1.5)}{0.5\times10^{-3}}=1.8$ mm; the 3rd bright fringe sits at $3\beta=5.4$ mm from the centre.