In Fig. 35-51a, the waves along rays 1 and 2 are initially...

In Fig. 35-51a, the waves along rays 1 and 2 are initially in phase, with the same wavelength $\lambda$ in air. Ray 2 goes through a material with length $L$ and index of refraction $n .$ The rays are then reflected by mirrors to a common point $P$ on a screen. Suppose that we can vary $L$ from 0 to $2400 \mathrm{nm}$. Suppose also that, from $L=0$ to $L_{s}=900 \mathrm{nm}$ the intensity $I$ of the light at point $P$ varies with $L$ as given in Fig. $35-52$. At what values of $L$ greater than $L_{\mathrm{s}}$ is intensity $I$ (a) maximum and (b) zero? (c) What multiple of $\lambda$ gives the phase difference between ray 1 and ray 2 at common point $P$ when $L=1200 \mathrm{nm} ?$

Key Concepts

Phase Difference

This refers to the difference in the phases of two light waves when they interfere. It arises due to differences in their optical path lengths, which can result from traveling through different media or distances. The phase difference determines whether the interference at a point is constructive or destructive.

Optical Path Length

This is the effective distance that light travels in a medium, taking into account the refractive index. When light enters a material with refractive index n, its speed decreases, effectively increasing the optical path length compared to the physical distance. This concept is used to determine the phase accumulated by the wave as it travels through the medium.

Index of Refraction

This is a measure of how much the speed of light is reduced inside a medium compared to its speed in a vacuum. It plays a crucial role in calculating the optical path length since the effective wavelength in the medium is the wavelength in vacuum divided by the index of refraction, thereby influencing the phase difference between beams.

Interference Conditions

These are the criteria that define when two light waves will interfere constructively (resulting in maximum intensity) or destructively (resulting in zero intensity). Constructive interference typically occurs when the phase difference is an integer multiple of 2? (or when the optical path difference is an integer multiple of the wavelength), while destructive interference occurs when the phase difference is an odd multiple of ? (or when the optical path difference is a half-integer multiple of the wavelength).

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