Tag: speed of light and optical density

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Questions Related to speed of light and optical density

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

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.

  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. $\displaystyle v _B=\frac{1}{2}(v _A+v _C)$
Reveal answer Fill a bubble to check yourself
C,D Correct answer
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.

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

Which of the following properties of light conclusively support wave theory of 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
Reveal answer Fill a bubble to check yourself
B Correct answer
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.
Multiple choice physics option a: relativity the nature of light speed of light and optical density introduction to light

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

  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.
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

The electromagnetic waves

  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.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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

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

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

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

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

All colours travel with the same speed in :

  1. Vaccum

  2. Glass 

  3. Water

  4. All of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a vacuum, the refractive index is 1 for all frequencies, so all colors (wavelengths) travel at the same speed c. In media like glass or water, dispersion occurs, meaning speed depends on the refractive index, which varies with wavelength.

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

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

  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
Reveal answer Fill a bubble to check yourself
C Correct answer
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

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

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

  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 } } } $
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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 $3.00\times 10^8 m/s$

  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. $1.4\times 10^{-6}Hz$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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

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)?

  1. $150\ nm$

  2. $200\ nm$

  3. $300\ nm$

  4. $400\ nm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For constructive interference in a thin film (n_oil=1.2, n_glass=1.6, n_air=1.0), there is a phase shift at both surfaces. The condition for constructive interference is 2nt = m * lambda. For minimum thickness, m=1: 2 * 1.2 * t = 480 nm. t = 480 / 2.4 = 200 nm.