Find the height h of the pits on a CD (Fig. 25.6a). When the...

Find the height $h$ of the pits on a CD (Fig. 25.6a). When the laser beam reflects partly from a pit and partly from land (the flat aluminum surface) on cither side of the pit, the two reflected beams interfere destructively; $h$ is chosen to be the smallest possible height that causes destructive interference. The wavelength of the laser is $780 \mathrm{nm},$ and the index of refraction of the polycarbonate plastic is $n=1.55$

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Key Concepts

Optical Path Length

The optical path length is the product of the physical distance traveled by light in a medium and the refractive index of that medium. It determines the phase shift experienced by the light, which is crucial when considering interference effects between beams that have taken different paths.

Index of Refraction

The index of refraction indicates how much the speed of light is reduced inside a medium compared to its speed in a vacuum. It directly affects the wavelength of light within the material and is essential for calculating the correct optical path difference needed to achieve the desired interference condition.

Destructive Interference

Destructive interference occurs when two waves combine with a phase difference such that their amplitudes cancel each other. In the context of optical devices, this is achieved when the phase difference between two reflected beams equals an odd multiple of ½ wavelengths, resulting in minimal or zero net reflected intensity.

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