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When a film is illuminated by white light, its upper portion appears dark, Path difference between two reflected beams at the spot must be
A. zero
B. $\lambda /2$
C. $2\lambda /2$
D. $\pi $

Last updated date: 16th Jul 2024
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Hint:-In order to this question, to calculate the path difference between two reflected beams at the spot, we will first explain the path difference and then go for the actual context of the question.

Complete step by step answer:
Firstly, we will explain the path difference, then only we will go to calculate the Path difference between two reflected beams at the spot. When waves from one source collide with waves from another, two-point source interference occurs. If the source of the waves is circular, the circular wavefronts will collide within the medium, forming a pattern.

The pattern is described by a set of nodes and antinodes that are connected by antinodal lines and nodal lines, which are nearly straight lines. There would be an antinodal line in the exact middle of the pattern and an alternating sequence of nodal and antinodal lines to the left and right of the central antinodal line if the wave sources have equal frequencies.

For the dark band, path difference is:
$x = (2N - 1)\dfrac{\lambda }{2}.......N = 1,2,......$
$\therefore x = \dfrac{\lambda }{2},\dfrac{{3\lambda }}{2},\dfrac{{5\lambda }}{2},.........$
Here, $x$ is the path difference.

Hence, the correct option is B.

Note:Now, we will explain here that why path difference has an importance, so in order to account for light interference and diffraction, the principle of path difference is critical. The direction difference of the photons, or pencils of rays, passing through the systems is used to calculate the distribution of luminous energy in optical systems.