Wave Optics: Interference and Diffraction

Young's Double-Slit & Diffraction

Shine light through two close slits and the screen shows stripes, places where light plus light equals darkness. Only waves can cancel.

Young's double-slit uses slits separated by $d$ to create distinct patterns:

Fringe Type	Formula	Condition
Bright	$d\sin\theta = m\lambda$	$m = 0, \pm 1, \pm 2$
Dark	$d\sin\theta = (m+\tfrac{1}{2})\lambda$	$m = 0, \pm 1, \pm 2$

Single-slit diffraction uses slit width $a$ where dark fringes obey $a\sin\theta = m\lambda$ .

Diffraction grating uses $N$ slits to give sharper maxima with resolution $R = mN$ .

The extra distance to one slit is the whole story

Thin-Film & Resolution Limits

Thin-film interference combines path difference $\Delta = 2nt$ with reflection shifts at higher- $n$ boundaries, adding an extra $\lambda/2$ phase change.

Reflection Shifts	Constructive Interference
One shift	$2nt = (m+\tfrac{1}{2})\lambda$
Zero or two shifts	$2nt = m\lambda$

Telescope resolution is limited by diffraction: $\theta_{\min} = 1.22\lambda/D$ .

Common pitfall: Interference never destroys energy. Dark fringes are matched by doubly-bright ones; energy is only redistributed, never lost.

Young's Double-Slit & Diffraction

Thin-Film & Resolution Limits

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Principles of Electromagnetism and Optics