Physical (wave) optics

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Light can be described as a wave - In vacuum, a sinusoidal wave train of light consists of a sinusoidal electric field wave train and a sinusoidal magnetic field wave train. The electric and magnetic field waves are transverse (axes of oscillation perpendicular to direction of propagation), and the electric and magnetic field oscillations are perpendicular to each other. The axis of polarization of light is the axis of polarization of the electric field. Speed of light in vacuum – The speed of propagation through a vacuum for both the electric field wave and the magnetic field wave is called 𝑐𝑐.

𝑐𝑐 = 3.00 × 108 ms

Brightness – Amplitude corresponds to intensity, and increasing intensity corresponds to increasing brightness.

𝐼𝐼 ∝ 𝐴𝐴2

↑ amplitude ⇒↑ brightness

Color - Frequency and (associated vacuum) wavelength correspond to color.

Just as has been the case for other waves we have encountered in AP Physics, frequency and wavelength are inversely proportional.

𝑐𝑐 = 𝜆𝜆𝜆𝜆

Physical (wave) optics

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Double-slit interference

For small angle 𝜃𝜃 (𝑥𝑥 ≪ 𝐿𝐿),

Bright maxima

Dark minima

𝑛𝑛𝜆𝜆𝑑𝑑 ≅ sin𝜃𝜃 ≅

𝑥𝑥𝐿𝐿

𝑛𝑛 = 0,1,2, …

�𝑛𝑛 −12�

𝜆𝜆𝑑𝑑 ≅ sin𝜃𝜃 ≅

𝑥𝑥𝐿𝐿

𝑛𝑛 = 1,2,3, …

Single-aperture interference

For small angle 𝜃𝜃 (𝑥𝑥 ≪ 𝐿𝐿),

Bright maxima (except central maximum)

Dark minima

�𝑛𝑛 +12�

𝜆𝜆𝑑𝑑 ≅ sin𝜃𝜃 ≅

𝑥𝑥𝐿𝐿

𝑛𝑛 = 1,2,3, …

𝑛𝑛𝜆𝜆𝑑𝑑 ≅ sin𝜃𝜃 ≅

𝑥𝑥𝐿𝐿

𝑛𝑛 = 1,2,3, …