Answer
418.5k+ views
Hint: We are given a system in which a source, a slit, a mirror, and a screen. We need to find the fringe width of the fringes formed by this system which can be easily calculated by using Young’s double-slit experiment approach to this.
Complete step by step solution:
We know that Young’s double-slit experiment involves a pair of sources of coherent waves, which interfere at a point on the given screen to form the fringes. Here, we are given only one source and instead of a second source, a mirror has been installed in the path of the light.
We know that light rays from a source when falling on the mirror reflects and takes a different path. If we extend this path, we will get a point S’ which is a mirror image of the actual slit S. This slit S’ will be the virtual second source for our modified version of Young’s Double Slit Experiment. The highlighted colors in the figure show the extended rays.
We understand that now we can consider this as Young’s double-slit experiment for further calculation.
We need to find the fringe width of the interference pattern formed by this system. We know that the fringe width is independent of the fringe number. It only depends on the wavelength of the light, the distance D from the screen to the slits, and the slit width d.
i.e.,
The fringe width is given as –
\[\beta =\dfrac{\lambda D}{d}\]
We can find the fringe width as –
\[\begin{align}
& \beta =\dfrac{\lambda D}{d} \\
& \lambda =500\times {{10}^{-9}}m \\
& D=2m \\
& d=2\times {{10}^{-3}}m \\
& \Rightarrow \beta =\dfrac{500\times {{10}^{-9}}\times 2}{2\times {{10}^{-3}}} \\
& \therefore \beta =0.05cm \\
\end{align}\]
The fringe width of the given arrangement will be 0.05cm.
The correct answer is option A.
Note: The Young’s Double Slit experiment can be manipulated in any way such as to get two sources of coherent waves. The fringe width in a given setup is highly dependent on the physical parameters like the distances involved. We should be careful about the arrangement.
Complete step by step solution:
We know that Young’s double-slit experiment involves a pair of sources of coherent waves, which interfere at a point on the given screen to form the fringes. Here, we are given only one source and instead of a second source, a mirror has been installed in the path of the light.
We know that light rays from a source when falling on the mirror reflects and takes a different path. If we extend this path, we will get a point S’ which is a mirror image of the actual slit S. This slit S’ will be the virtual second source for our modified version of Young’s Double Slit Experiment. The highlighted colors in the figure show the extended rays.
We understand that now we can consider this as Young’s double-slit experiment for further calculation.
![seo images](https://www.vedantu.com/question-sets/f4462af8-0b82-4633-aa67-4aa8f359473f5908830731745687358.png)
We need to find the fringe width of the interference pattern formed by this system. We know that the fringe width is independent of the fringe number. It only depends on the wavelength of the light, the distance D from the screen to the slits, and the slit width d.
i.e.,
The fringe width is given as –
\[\beta =\dfrac{\lambda D}{d}\]
We can find the fringe width as –
\[\begin{align}
& \beta =\dfrac{\lambda D}{d} \\
& \lambda =500\times {{10}^{-9}}m \\
& D=2m \\
& d=2\times {{10}^{-3}}m \\
& \Rightarrow \beta =\dfrac{500\times {{10}^{-9}}\times 2}{2\times {{10}^{-3}}} \\
& \therefore \beta =0.05cm \\
\end{align}\]
The fringe width of the given arrangement will be 0.05cm.
The correct answer is option A.
Note: The Young’s Double Slit experiment can be manipulated in any way such as to get two sources of coherent waves. The fringe width in a given setup is highly dependent on the physical parameters like the distances involved. We should be careful about the arrangement.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)