Tag: speed of light and optical density

Questions Related to speed of light and optical density

Three observers $A,B$ and $C$ measure the speed of light coming from a source to be $v _A,v _B$ and $v _C$. The observer $A$ moves towards the source and $C$ moves away from the source at the same speed. The observer $B$ stays stationary. The surrounding space is vacuum everywhere.

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

  1. $\displaystyle v _A>v _B>v _C$

  2. $\displaystyle v _A < v _B < v _C$

  3. $\displaystyle v _A=v _B=v _C$

  4. $\displaystyle v _B=\frac{1}{2}(v _A+v _C)$

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Correct Option: C,D
Explanation:

Relativity states that the speed of light in vacuum will be same independent of the frame of reference. The frame of reference can be stationary or moving.
So all  three will find the speed of light to be $ c $
Also $ c=\dfrac{1}{2}(c+c) $
So, (C) and (D) are correct.

Which of the following properties of light conclusively support wave theory of light?

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

  1. Light obeys laws of reflection

  2. Speed of light in water is smaller than the speed in vacuum

  3. Light doesn't show interferrence

  4. Light shows photoelectric effect

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Correct Option: B
Explanation:
Laws of reflection was successfully explained by both wave theory and corpuscular theory of light.
Only Speed of light in water is smaller than the speed in vacuum was was proven by wave theory of light.

An electromagnetic wave of frequency $v=3.0:MHz$ passes from vacuum into a dielectric medium with permittivity $\epsilon=4.0$. Then

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

  1. wavelength is halved and frequency remains unchanged.

  2. wavelength is doubled and frequency becomes half.

  3. wavelength is doubled and frequency remains unchanged.

  4. wavelength and frequency both remain unchanged.

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Correct Option: A
Explanation:

Frequency remains constant during refraction.

$\displaystyle v _{med}=\dfrac{1}{\sqrt{\mu _0\epsilon _0\times4}}=\dfrac{c}{2}$

$\displaystyle\dfrac{\lambda _{med}}{\lambda _{air}}=\dfrac{v _{med}}{v _{air}}=\dfrac{\displaystyle\dfrac{c}{2}}{c}=\dfrac{1}{2}$

$\therefore$ wavelength is halved and frequency remains unchanged.

The electromagnetic waves

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

  1. travel with the the speed of sound.

  2. travel with the the same speed in all media.

  3. travel in free space with the speed of light.

  4. do not travel through a medium.

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Correct Option: C
Explanation:

The electromagnetic waves of all wavelengths travel with the same speed in space which is equal to velocity of light.

The apparent wavelength of light from a star moving away from the earth is 0.02% more than actual wavelength. What is the velocity of the star.

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

  1. $\displaystyle 30{ kms }^{ -1 }$

  2. $\displaystyle 60{ kms }^{ -1 }$

  3. $\displaystyle 90{ kms }^{ -1 }$

  4. None of these

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Correct Option: B
Explanation:

Answer is B.

The apparent change in the wavelength is given as follows.
$\displaystyle \frac { \Delta \lambda  }{ \lambda  } =\frac { v }{ C } ,Hence\quad V=\frac { \Delta \lambda  }{ \lambda  } C$
$\displaystyle =\frac { 0.02 }{ 100 } \times 3\times { 10 }^{ 8 }{ ms }^{ -1 }=60{ kms }^{ -1 }$.
Hence, the velocity of the star is 60 km/s.

All colours travel with the same speed in :

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

  1. Vaccum

  2. Glass 

  3. Water

  4. All of the above

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Correct Option: A

An electromagnetic wave of frequency $\mathrm{v}=3.0$ MHz passes from vacuum into a dielectric medium with permittivity $\epsilon =4.0$. Then : 

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

  1. wavelength is doubled and frequency remains unchanged

  2. wavelength is doubled and frequency becomes half

  3. wavelength is halved and frequency remains unchanged

  4. wavelength and frequency both remain unchanged

Show answer
Correct Option: C
Explanation:

$f=3.0mHz$

$E=4.0$

$C=fZ$

C is the speed of light into the medium

${ C } _{ 0 }=f _{ i }{ Z } _{ i }  C=\dfrac { { C } _{ 0 } }{ n } \\ C={ f } _{ f }{ Z } _{ f }  n=\sqrt { \dfrac { \varepsilon }{ { \varepsilon } _{ 0 } } } \\ C=\dfrac { { C } _{ 0 } }{ 2 } $

Now since frequency depends on source

Hence ${ f } _{ f }={ f } _{ i }\\ { Z } _{ f }=\dfrac { { Z } _{ i } }{ 2 } $

Speed and wavelength will be halved

The velocity of electromagnetic radiation in a medium of permittivity ${\varepsilon} _{0}$ and permeability ${\mu} _{0}$ is given by :

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

  1. $\sqrt { \dfrac { { \varepsilon } _{ 0 } }{ { \mu } _{ 0 } } } $

  2. $\sqrt { { \mu } _{ 0 }{ \varepsilon } _{ 0 } } $

  3. $\dfrac { 1 }{ \sqrt { { \mu } _{ 0 }{ \varepsilon } _{ 0 } } } $

  4. $\sqrt { \dfrac { { \mu } _{ 0 } }{ { \varepsilon } _{ 0 } } } $

Show answer
Correct Option: C
Explanation:

Velocity of electromagnetic radiation is the velocity of light $\left(c\right)$, i.e.,
$c=\dfrac { 1 }{ \sqrt { { \mu  } _{ 0 }{ \varepsilon  } _{ 0 } }  } $
where ${ \mu  } _{ 0 }$ is the permeability and ${ \varepsilon  } _{ 0 }$ is the permittivity of free space.

A certain color of light towards the purple end of the visible spectrum has a wavelength of $420\ nm$ in a vacuum.
What is the frequency of this light?
The speed of light in a vacuum is $3.00\times 10^8 m/s$

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

  1. $126 Hz$

  2. $1.26\times 10^{11}Hz$

  3. $7.1\times 10^{14}Hz$

  4. $1.4\times 10^{-15}Hz$

  5. $1.4\times 10^{-6}Hz$

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Correct Option: C
Explanation:

Given :   $v = 3.00 \times 10^8$  m/s                 $\lambda = 420$ nm $ = 420 \times 10^{-9}$  m

$\therefore$ Frequency of the light       $\nu = \dfrac{v}{\lambda} = \dfrac{3.00 \times 10^8}{420 \times 10^{-9}} = 7.1 \times 10^{14}$  $Hz$

Blue light of wavelength $480\ nanometers$, is most strongly reflected off a thin film of oil on a glass slide, when viewed near normal incidence. Assuming that the index of refraction of the oil is $1.2$ and that of the glass is $1.6$, what is the minimum thickness of the oil film (other than zero)?

physics refraction of light the nature of light speed of light and optical density introduction to light

  1. $150\ nm$

  2. $200\ nm$

  3. $300\ nm$

  4. $400\ nm$

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Correct Option: B