Answer
358.2k+ views
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.
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.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Other Pages
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Electric field due to uniformly charged sphere class 12 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
According to classical free electron theory A There class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)