Answer
Verified
413.1k+ views
Hint: Here we are using the fact that the speed of light is dependent upon the relative electric permittivity. Also we take into consideration that the permittivity for each material will be different. Then we will use the definition of refractive index to find out the refractive index of glass.
Complete step by step answer:
The speed of light in glass is given by, $r = \,\dfrac{1}{{\sqrt {\varepsilon \,\mu } }}$
Here,${\varepsilon _g}$ is the permittivity of glass (The dielectric constant)
${\mu _g}$ is the relative magnetic permeability of glass
We put these values in the above equation of speed of light in glass.
\[r = \,\dfrac{1}{{\sqrt {{\varepsilon _g}{\varepsilon _ \circ }\,{\mu _g}{\mu _ \circ }} }}\]
If we separate out the factor of \[\dfrac{1}{{\sqrt {{\varepsilon _ \circ }\,{\mu _ \circ }} }}\] from the above equation, we get
\[r = \,\dfrac{1}{{\sqrt {{\varepsilon _ \circ }\,{\mu _ \circ }} }} \times \dfrac{1}{{\sqrt {{\varepsilon _g}\,{\mu _g}} }}\]as we have the speed of light as $c = \,\dfrac{1}{{\sqrt {{\varepsilon _ \circ }{\mu _ \circ }} }}$. Here, ${\mu _o}$ is the magnetic permeability of free space and ${\varepsilon _o}$ is the permittivity of free space.
Now, we will put this in the equation and we get,
\[r = \,c \times \dfrac{1}{{\sqrt {{\varepsilon _g}\,{\mu _g}} }}\]
After rearranging the equation, the equation becomes,
\[\dfrac{c}{r} = \,\sqrt {{\varepsilon _g}\,{\mu _g}} \]
Now, putting values given in the Question, we get
\[
\dfrac{c}{r} = \sqrt {\dfrac{3}{8} \times 8} \\
\Rightarrow\dfrac{c}{r} = \sqrt 3 \\
\Rightarrow\dfrac{c}{r} = 1.732
\]
The refractive index of glass:
$
\dfrac{{{\rm{speed}}\,{\rm{of}}\,{\rm{light in vacuum}}}}{{{\rm{speed of light in glass}}}} = \dfrac{c}{r}\\
\therefore\dfrac{{{\rm{speed}}\,{\rm{of}}\,{\rm{light in vacuum}}}}{{{\rm{speed of light in glass}}}} = 1.732
$
Therefore, the refractive index of glass is 1.732, and the correct option is C.
Additional information:
The Electromagnetic waves have wavelength and frequency whose product gives the speed of the light in free space. The refractive index for air is 1 for all wavelengths. When an EM wave travels from one medium to another medium with a different refractive index, then the speed of the wave changes as well as wavelength. But the frequency does not change.
Note:The calculation of speed of light is done with consideration of the electric permittivity of free space and magnetic permeability of free space. In this formula of refractive index of glass, the speed of a wave in a vacuum should be in the numerator at all times.
Complete step by step answer:
The speed of light in glass is given by, $r = \,\dfrac{1}{{\sqrt {\varepsilon \,\mu } }}$
Here,${\varepsilon _g}$ is the permittivity of glass (The dielectric constant)
${\mu _g}$ is the relative magnetic permeability of glass
We put these values in the above equation of speed of light in glass.
\[r = \,\dfrac{1}{{\sqrt {{\varepsilon _g}{\varepsilon _ \circ }\,{\mu _g}{\mu _ \circ }} }}\]
If we separate out the factor of \[\dfrac{1}{{\sqrt {{\varepsilon _ \circ }\,{\mu _ \circ }} }}\] from the above equation, we get
\[r = \,\dfrac{1}{{\sqrt {{\varepsilon _ \circ }\,{\mu _ \circ }} }} \times \dfrac{1}{{\sqrt {{\varepsilon _g}\,{\mu _g}} }}\]as we have the speed of light as $c = \,\dfrac{1}{{\sqrt {{\varepsilon _ \circ }{\mu _ \circ }} }}$. Here, ${\mu _o}$ is the magnetic permeability of free space and ${\varepsilon _o}$ is the permittivity of free space.
Now, we will put this in the equation and we get,
\[r = \,c \times \dfrac{1}{{\sqrt {{\varepsilon _g}\,{\mu _g}} }}\]
After rearranging the equation, the equation becomes,
\[\dfrac{c}{r} = \,\sqrt {{\varepsilon _g}\,{\mu _g}} \]
Now, putting values given in the Question, we get
\[
\dfrac{c}{r} = \sqrt {\dfrac{3}{8} \times 8} \\
\Rightarrow\dfrac{c}{r} = \sqrt 3 \\
\Rightarrow\dfrac{c}{r} = 1.732
\]
The refractive index of glass:
$
\dfrac{{{\rm{speed}}\,{\rm{of}}\,{\rm{light in vacuum}}}}{{{\rm{speed of light in glass}}}} = \dfrac{c}{r}\\
\therefore\dfrac{{{\rm{speed}}\,{\rm{of}}\,{\rm{light in vacuum}}}}{{{\rm{speed of light in glass}}}} = 1.732
$
Therefore, the refractive index of glass is 1.732, and the correct option is C.
Additional information:
The Electromagnetic waves have wavelength and frequency whose product gives the speed of the light in free space. The refractive index for air is 1 for all wavelengths. When an EM wave travels from one medium to another medium with a different refractive index, then the speed of the wave changes as well as wavelength. But the frequency does not change.
Note:The calculation of speed of light is done with consideration of the electric permittivity of free space and magnetic permeability of free space. In this formula of refractive index of glass, the speed of a wave in a vacuum should be in the numerator at all times.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
A group of fish is known as class 7 english CBSE
The highest dam in India is A Bhakra dam B Tehri dam class 10 social science CBSE
Write all prime numbers between 80 and 100 class 8 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Onam is the main festival of which state A Karnataka class 7 social science CBSE
Who administers the oath of office to the President class 10 social science CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Kolkata port is situated on the banks of river A Ganga class 9 social science CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE