Tag: the nature of light

Quizzes (0) Questions (83)

Questions Related to the nature of light

Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

According to Maxwell's hypothesis, changing of electric filed give rise to

  1. magnetic field

  2. pressure gradient

  3. charge

  4. voltage
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to Maxwell's hypothesis, changing of electric field gives rise to Magnetic field.

We know that $F=qE,$, where $F$ is force and $E$ is electric field.
We can relate magnetic field and force by $F=qvB$, where $v$ is velocity and $B$ is the magnetic field.
Therefore we can obtain magnetic field by changing electric field.
Therefore option $A$ is correct.

Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

Unpolarized light falls first on polarizer $\left( P \right) $ and then on analyzer $\left( A \right) $. If the intensity of the transmitted light from the analyser is $\dfrac { 1 }{ 8 }$th of the incident unpolarized light. What will be the angle between optic axes of $P$ and $A$?

  1. ${ 45 }^{ o }$

  2. ${ 30 }^{ o }$

  3. Zero

  4. ${ 60 }^{ o }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given,
$I=\dfrac { { I } _{ 0 } }{ 2 } $              ....(i)
${ I }^{ ' }=I\cos ^{ 2 }{ \theta  } $                 $\left( \because { I }^{ ' }=\dfrac { { I } _{ 0 } }{ 8 }  \right) $
$\therefore \dfrac { { I } _{ 0 } }{ 8 } =\dfrac { { I } _{ 0 } }{ 2 } \cos ^{ 2 }{ \theta  } $
From the equation (i), we have
$\dfrac { 1 }{ 4 } =\cos ^{ 2 }{ \theta  } \Rightarrow \cos { \theta  } ={ 1 }/{ 2 }$
$\Rightarrow \cos { \theta  } =\cos { { 60 }^{ o } } $
$\Rightarrow \theta ={ 60 }^{ o }$

Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

A plane electromagnetic wave with an intensity of $200 W/m^2$ is incident normal to a flat plate of radius 30 cm. If the plate absorbs $60%$ and reflect $40%$ of the incident radiation, what is the momentum transferred to it in 5 min?

  1. $1.7 \times 10^{-3} kg ms^{-1}$

  2. $2.7 \times 10^{-4} kg ms^{-1}$

  3. $3.7 \times 10^{-4} kg ms^{-1}$

  4. $3.7 \times 10^{-3} kg ms^{-1}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics option a: relativity the nature of light speed of light and optical density introduction to light

Choose the correct answer from the alternatives given.
An electromagnetic wave of frequency $\nu= 3\ MHz$ passes from vacuum  into a dielectric medium with permittivity $\varepsilon= 4$. Then

  1. wavelength and frequency both become half.

  2. wavelength is doubled and frequency remains unchanged.

  3. wavelength and frequency both remain unchanged.

  4. wavelength is halved and frequency remains unchanged.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given : frequency $v =3 MHz=3\times10^6Hz$, relative permitivity $\varepsilon _r = 4$
Here the frequency of electromagnetic wave remains unchanged but the wavelength of electromagnetic wave changes when it passes from one medium to another.
The refractive index is the square root of permeability and permittivity product. 
For formula,
$c=\dfrac 1{\sqrt {\mu _0\varepsilon _0}}\\\implies c\propto \dfrac1{\sqrt{\varepsilon _0}}$
Similarly,
$v\propto\dfrac1{\sqrt{\varepsilon}}$
Therefore,
$\dfrac cv=\sqrt{\dfrac {\varepsilon}{\varepsilon _0}}=\sqrt{\dfrac 41}=2........(i)$
But
$\dfrac cv=\dfrac {\nu\lambda}{\nu\lambda'}\\\implies \dfrac cv=\dfrac{\lambda}{\lambda'}\\\implies 2=\dfrac{\lambda}{\lambda'}\\\implies \lambda'=\dfrac \lambda2$
Hence wavelength is halved.
Multiple choice physics option a: relativity the nature of light speed of light and optical density introduction to light

An electromagnetic wave is propagating along x-axis. At x = 1 m and t = 10 s, its electric vector |$\overset{-}{E}|  = 6 V/m$ then the magnitude of its magnetic vector is:

  1. $2 \, \times \, 10^{-8} \, T$

  2. $3 \, \times \, 10^{-7} \, T$

  3. $6 \, \times \, 10^{-8} \, T$

  4. $5 \, \times \, 10^{-7} \, T$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Electric and magnetic compounds of an electromagnetic field are related by 

$E = CB$
$B = \dfrac{E}{C}$
$B = \dfrac{6}{3 \times 10^8}$  (when $E$ is given)
$B = 2 \times 10^{-8} T$ 

Multiple choice physics option a: relativity the nature of light speed of light and optical density introduction to light

The electric field associated with an electromagnetic wave in vacuum is given by $|\overrightarrow { E } |= 40\ cos (kz -6\times{10}^{8}t )$, where $E$, $z$ and $t$ are in volt per meter, meter and second respectively. The value of wave vector $k$ is:

  1. $2\ {m}^{-1}$

  2. $0.5\ {m}^{-1}$

  3. $3\ {m}^{-1}$

  4. $6\ {m}^{-1}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given: The electric field associated with  an electromagnetic wave in vacuum is given by $|\vec E|=40 \cos(kz−6\times 10^8t)$


To find: Value of wave vector $k$


Solution: 
We know electromagnetic wave eqution is
$|\vec E|=E _0\cos(kz-\omega t)$

And given equation is
$|\vec E|=40 \cos(kz−6\times 10^8t)$

By comparing these two, we get
$\omega=6\times10^8$ and 
$E _0=40$

We also know,
Speed of electromagnetic wave is given by:
$v=\dfrac \omega k$
where v is the speed of the light.

Hence, 
$k=\dfrac \omega v\\\implies k=\dfrac {6\times 10^8}{3\times 10^8}\\\implies k=2m^{-1}$

Option $(A)$ is correct.

Multiple choice physics option a: relativity the nature of light speed of light and optical density introduction to light

The velocity of electromagnetic waves in a dielectric medium $\left( { \varepsilon  } _{ r }=2 \right) $ is:

  1. $3\times { 10 }^{ 8 }$ meter/second

  2. $1.5\times { 10 }^{ 8 }$ meter/second

  3. $6\times { 10 }^{ 8 }$ meter/second

  4. $7.5\times { 10 }^{ 7 }$ meter/second
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
It turns out that electromagnetic waves cannot propagate very far through a conducting medium before they are either absorbed or reflected. However, electromagnetic waves are able to propagate through transparent dielectric media without difficultly. The speed of electromagnetic waves propagating through a dielectric medium is given by 
$c'=\dfrac{c}{\epsilon _r}$
Multiple choice physics option a: relativity the nature of light speed of light and optical density introduction to light

If the relative permeability of a medium is $ \mu _r$ and its dielectric constant is  $\varepsilon _r$ then the velocity of light in that medium will be

  1. $ \sqrt{\dfrac { \mu _r }{ { { \varepsilon } _{ r } } }} $

  2. $ \dfrac { 1 }{ \sqrt { { \mu } _{ r }{ \varepsilon } _{ r } } } $

  3. $ \sqrt { { \mu } _{ r }{ \varepsilon } _{ r }/{ \mu } _{ { \varepsilon } _{ 0 } } } $

  4. $ \sqrt { { \mu } _{ 0 }{ \varepsilon } _{ 0 }/{ \mu } _{ { r } }{ \varepsilon } _{ r } } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$c=\dfrac{1}{\sqrt{\epsilon _0\mu _0}}$

$v=\dfrac{1}{\sqrt{\epsilon\mu}}=\dfrac{1}{\sqrt{\epsilon _0\epsilon _r\mu _0\mu _r}}$
$=\dfrac{c}{\sqrt{\epsilon _r\mu _r}}$

Multiple choice physics option a: relativity the nature of light speed of light and optical density introduction to light

The speed of electromagnetic wave in vacuum depends upon the source of radiation. It

  1. increases as we move from $\gamma$-rays to radio waves

  2. decreases as we move from $\gamma$-rays to radio waves

  3. is same for all of them

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$Answer:-$ C

speed of electromagnetic wave in vacuum  is given by:-
c(speed of light)=frequency$\times$ wavelength =$\dfrac{1}{\mu _0 \epsilon _0}$=constant
as we go from gamma rays to radio waves  frequency decreases and wavelength increases thereby maintaining the product constant.