Question

The central fringe of interference pattern produced by light of wavelength $6000$ A Is found to shift to the position of 4th bright fringe, after a glass plate of $\mu = 1.5$ is introduced. The thickness of the glass plate is:
A) $4.8\mu m$
B) $8.23\mu m$
C) $14.98\mu m$
D) $3.78\mu m$

Answer 1

Hint: Shift at ${n^{th}}$ bright fringe is $(\mu - 1)t = n\lambda $ (where, $\mu $ is the refractive index of the glass plate, $t$ is the thickness of the glass plate, $\lambda $ is the wavelength of the light).

Complete step by step answer:
When two light waves of the same frequency and amplitude superpose in a certain region of a medium, the intensity of the resultant light wave increases at certain points and decreases at some other points in that region. This phenomenon is known as the interference of light and these alternate dark and bright lines are called interference fringes.
According to the formula, shift at ${n^{th}}$ bright fringe is $(\mu - 1)t = n\lambda $ (where, $\mu $ is the refractive index of the glass plate, $t$ is the thickness of the glass plate, $\lambda $ is the wavelength of the light.)
Putting all the given values in the equation, we get,
$(1.5 - 1)t = 4(6000 \times {10^{ - 10}})$
$\implies t = \dfrac{{4(6000 \times {{10}^{ - 10}})}}{{0.5}} = 4.8 \times {10^{ - 10}}m = 4.8\mu m$
So, the thickness of the glass plate is $4.8\mu m$.
$\therefore$ The correct option is A.

Additional Information: In an interference pattern, there is no loss or destruction of light energy in the dark fringes area. The energy just gets shifted from the region of the dark band to the region of the bright band. Total energy remains the same. It can be shown that the average intensity of a set of simultaneous consecutive dark and bright fringes is the same as the intensity of the usual illumination in the same region. Hence, we can say that the interference fringe does not contradict the law of conservation of energy.

Note: It is to be noted that, when light travels through a medium, the equivalent optical path of the actual path traveled by light is the product of the refractive index of the medium and the actual path traveled. Also, though a displacement occurs in fringe pattern due to insertion of a glass plate, fringe width remains unaltered.