Tag: the nature of light

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Questions Related to the nature of light

Multiple choice physics observing space: telescopes maxwell's equations the nature of light introduction to electromagnetic waves

In vacuum, electromagnetic waves travel at the speed of

  1. $3 \times {10}^{8} {m}/{s}$

  2. $3 \times {10}^{6} {m}/{s}$

  3. $3 \times {10}^{-8} {m}/{s}$

  4. $3 \times {10}^{18} {m}/{s}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In vacuum, electromagnetic waves travel at speed of $3\times { 10 }^{ 8 }$ m/s.

C = speed of EM waves
C = $\frac { 1 }{ \sqrt { { \mu  } _{ 0 }{ \varepsilon  } _{ 0 } }  } $
                ${ \mu  } _{ 0 }$ = permaebility of free space
                ${ \varepsilon  } _{ 0 }$ = permittivity of free space
putting the value of ${ \mu  } _{ 0 }$ and ${ \varepsilon  } _{ 0 }$ we get value of C approximately $3\times { 10 }^{ 8 }$ m/s.
                ${ \mu  } _{ 0 }$ = $1.257\times { 10 }^{ -6 }$ Henry/meter
                ${ \varepsilon  } _{ 0 }$ = $8.85\times { 10 }^{ -12 }$ Farad/meter

Multiple choice physics observing space: telescopes maxwell's equations the nature of light introduction to electromagnetic waves

Reflection of a light wave at a fixed point results in a phase difference between incident and reflected wave of

  1. $\dfrac{3\pi}{2}$

  2. $2 \pi $ rad

  3. $\pi$ rad

  4. $\dfrac{\pi}{2}$ rad
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Reflection of light wave at fixed point result in phase difference b/w incident and reflected ray of $\pi$. The wave gets inverted. Inversion behavior is noticed when medium is connected to dense medium.

Multiple choice physics observing space: telescopes maxwell's equations the nature of light introduction to electromagnetic waves

Choose the correct answer from the alternatives given.


Which of the following has/have zero average value in a plane electromagnetic wave?

  1. Both magnetic and electric fields

  2. electric field only

  3. Magnetic field only

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

A. Both magnetic and electric field.


Because both electric and magnetic field oscillate as sine and cosine wave, which over one period, average value is zero.

Multiple choice physics observing space: telescopes maxwell's equations the nature of light introduction to electromagnetic waves

Which of the following statement is false for the properties of electromagnetic waves?

  1. Both electric and magnetic field vectors attain the maxima and minima at same place and same time.

  2. The energy in electromagnetic wave is divided equally between electric and magnetic field vectors.

  3. Both electric and magnetic field vectors are parallel to each other and perpendicular to the direction of propagation of wave.

  4. These waves do not require any material medium for propagation.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In electromagnetic waves,

1. The electric field and magnetic field varies continuously with time and have maxima and minima at same place and at same time.
2. Both electric and magnetic field have same energy.
3. both electric and magnetic field are perpendicular to each other and perpendicular to direction of propagation.
4. These waves don't require any material medium to propagate, they can propagate in vacuum as well.
So, the false statement will be the statement given in the option $(C)$
Hence, the correct option is $(C)$

Multiple choice physics observing space: telescopes maxwell's equations the nature of light introduction to electromagnetic waves

The electric field of a plane electromagnetic wave is given by
$\vec{E} = E _0 \dfrac{\hat{i} + \hat{j}}{\sqrt{2}} \cos (kz + \omega t)$
At $t = 0$, a positively charged particle is at the point $(x, y , z) = \left(0, 0 , \dfrac{\pi}{k} \right)$. If its instantaneous velocity at $(t = 0)$ is $v _0 \hat{k}$, the force acting on it due to the wave is :

  1. parallel to $\hat{k}$

  2. parallel to $\dfrac{\hat{i} + \hat{j}}{\sqrt{2}}$

  3. antiparallel to $\dfrac{\hat{i} + \hat{j}}{\sqrt{2}}$

  4. zero
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\vec{E} = E _0 \left(\dfrac{i + j}{\sqrt{2}}\right) \cos (kz + wt)$


$\therefore$ unit vector along electric field, $\vec{E} = \left(\dfrac{\hat{i} + \hat{j}}{\sqrt{2}} \right)$


Direction of electromagnetic wave is in (-z) direction 

$\therefore \hat{C} = -\hat{k}$  wave direction.

Let $\hat{B} $ is the unit vector along the direction of magnetic field.

$\hat{B} = \hat{C} \times \hat{E} = -\hat{k} \times \left(\dfrac{\hat{i} + \hat{j}}{\sqrt{2}} \right) = - \left(\dfrac{\hat{k} \times i + \hat{k} \times j}{\sqrt{2}} \right)$

$\hat{B} = -\left(\dfrac{\hat{j} + (-i)}{\sqrt{2}} \right)  = \left(\dfrac{\hat{i} - \hat{j}}{\sqrt{2}} \right)$

$\vec{F _e} =$ electric force on the charge particle 

$\vec{F _e} = $ unit vector of electric force $= \dfrac{q \hat{E}}{|q\hat{E}|} = \hat{E}$

$\vec{F} _e = \dfrac{\hat{i} + \hat{j}}{\sqrt{2}}$

$\vec{F} _b = $ magnetic force $= q \vec{V} \times \vec{B} = q \left(V _0 \hat{k} \times \dfrac{i - j}{\sqrt{2}}\right)$

$\vec{F} _b = q V _0 \left[\dfrac{\hat{k} \times \hat{i} - \hat{k} \times \hat{j}}{\sqrt{2}} \right] = q V _0 \left[\dfrac{\hat{j} - (-\hat{i})}{\sqrt{2}}\right]$

$\vec{F} _b = q V _0 \left(\dfrac{\hat{i} + \hat{j}}{\sqrt{2}} \right)$

$\vec{F} _{Net} = \hat{F} _e + \hat{F} _b = \dfrac{\hat{i} + \hat{j}}{\sqrt{2}} + \dfrac{\hat{i} + \hat{j}}{\sqrt{2}} = \dfrac{2}{\sqrt{2}} (\hat{i} + \hat{j})$

$\therefore \hat{F} _{Net} = $ unit vector $= \dfrac{\hat{i} + \hat{j}}{\sqrt{2}}$

Option (B) is correct.

Multiple choice physics observing space: telescopes maxwell's equations the nature of light introduction to electromagnetic waves

The Schrodinger equation for a free electron of mass m and energy E written in terms of the wave function $\psi $ is $\frac{d^2\psi}{dx^2}+\frac{8 \pi ^2mE}{h^2}\psi =0$. The dimensions of the coefficient $\psi$ of in the second term must be

  1. $[M^1L^1]$

  2. $[L^2]$

  3. $[L^{-2}]$

  4. $[M^1L^{-1}T^1]$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By dimensional analysis the dimensions of each term in an equation must be the same. In the first term the second derivative with respect to distance x indicates the dimensions of the coefficient $\psi$ of to be $[L^{-2}]$ and hence the answer.

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.

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

When light is refracted into a denser medium,

  1. its wavelength and frequency both increase

  2. its wavelength increases but frequency remains unchanged

  3. its wavelength decreases but frequency remains unchanged

  4. its wavelength and frequency both decrease
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$ _1\mu _2 = \dfrac{v _1}{v _2} = \dfrac{v _{rarer}}{v _{denser}} \Rightarrow v _1 > v _2$


$\Rightarrow v _1 > v _2$


$\Rightarrow \lambda _1 f _1 > \lambda _2 f _2$
Where $f$ is the frequency

when light goes from any rarer to any denser medium frequency remain unchanged.

$\therefore f _1 = f _2 = f$

$\Rightarrow \lambda _1 > \lambda _2$

hence wavelength decreases but frequency remains unchanged. 

Option C is correct.