Light having a vacuum wavelength of 600 nm, traveling in a glass (ng=1.50) block, is incident at

step 1 In this question we're given that a light is having wavelength of 600 nanometer in vacuum. It is

Light having a vacuum wavelength of 600 nm, traveling in a...

Light having a vacuum wavelength of $600 \mathrm{nm}$, traveling in a glass $\left(n_{g}=1.50\right)$ block, is incident at $45^{\circ}$ on a glass-air interface. It is then totally internally reflected. Determine the distance into the air at which the amplitude of the evanescent wave has dropped to a value of $1 / e$ of its maximum value at the interface.

Key Concepts

Refractive Index and Wavelength Relation

The refractive index of a medium affects the effective wavelength of light within that medium by reducing it relative to the vacuum wavelength. This relationship is essential for understanding how light behaves at interfaces, influencing phenomena such as phase shifts and the decay characteristics of evanescent waves.

Evanescent Wave

An evanescent wave is a non-propagating electromagnetic field that forms on the side of the interface where total internal reflection occurs. Although no energy is transmitted as a propagating wave into the lower refractive index medium, the evanescent field penetrates a short distance beyond the interface and undergoes exponential decay with distance.

Total Internal Reflection

Total internal reflection occurs when a light beam traveling in a medium with a higher refractive index meets an interface with a medium of lower refractive index at an angle greater than the critical angle. Under these circumstances, the light is completely reflected back into the original medium, and no propagating light passes into the second medium.

Penetration Depth

Penetration depth is the measure of the distance into the second medium at which the amplitude of the evanescent wave decays to 1/e of its maximum value at the interface. It characterizes how far the evanescent field extends and is determined by parameters such as the wavelength of light, the refractive indices of the media, and the angle of incidence.

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