Tag: polarisation of light

Questions Related to polarisation of light

A beam of unpolarized light is passed first through a tourmaline crystal $A$ and then through another tourmaline crystal $B$ oriented so that its principal plane is parallel to that of $A$. The intensity of final emergent light is $I$. The value of the $I$ is 

physics oscillations and waves polarization of light polarisation of light polarisation

  1. $\displaystyle\frac{I _o}{2}$

  2. $\displaystyle\frac{I _o}{4}$

  3. $\displaystyle\frac{I _o}{8}$

  4. none of these

Show answer
Correct Option: A
Explanation:

When the unpolarized light falls on the first tourmaline crystal, the intensity of the light halves and becomes polarized.

Thus $I _1=\dfrac{I _0}{2}$
When this polarized light falls on the next tourmaline crystal at an angle $\theta$, the intensity of light becomes,
$I _2=I _1cos^2\theta=I _1 cos^20^{\circ}$
$=\dfrac{I _0}{2}$

A beam of unpolarized light is passed first through a tourmaline crystal $A$ and then through another tourmaline crystal $B$ oriented so that its principal plane is parallel to that of $A$. The intensity of final emergent light is $I$. Flux of energy of the incident ray is $10^{-3}W$, the percentage of incident light transmitted by the second polarizered will be____

physics oscillations and waves polarization of light polarisation of light polarisation

  1. $12.5\%$

  2. $25\%$

  3. $37.5\%$

  4. $50\%$

Show answer
Correct Option: C

A beam of unpolarized light is passed first through a tourmaline crystal $A$ and then through another tourmaline crystal $B$ oriented so that its principal plane is parallel to that of $A$. The intensity of final emergent light is $I$. The intensity of the emergent beam, if flux of energy of the incident ray is $10^{-3}W$, will be (in $W/m^2$)

physics oscillations and waves polarization of light polarisation of light polarisation

  1. $\displaystyle\frac{I}{3}$

  2. $\displaystyle\frac{2I}{3}$

  3. $\displaystyle\frac{4I}{3}$

  4. $\displaystyle\frac{5I}{3}$

Show answer
Correct Option: D

A Plane polarized light is incidents on an analyzer. The intensity then becomes three-fourth. The angle of the axis of the analyzer with the beam is

physics oscillations and waves polarization of light polarisation of light polarisation

  1. $30^0$

  2. $45^0$

  3. $60^0$

  4. zero

Show answer
Correct Option: A
Explanation:

Intensity of light after passing through an analyzer which is at an angle $\theta$ with the beam,

$I=I _0\cos^2\theta$
$\implies \dfrac{3}{4}I _0=I _0\cos^2\theta$
$\cos\theta=\dfrac{\sqrt{3}}{2}$
$\implies \theta=30^{\circ}$

An unpolarized beam of light is incidents on a group of four polarizing sheets, which are arranged in such a way, that of the characteristic direction of each polarizing sheet makes an angle of $30^0$ with that of the preceding sheet. The percentage of incident light transmitted by the first polarizered will be :

physics oscillations and waves polarization of light polarisation of light polarisation

  1. $100\%$

  2. $50\%$

  3. $25\%$

  4. $12.5\%$

Show answer
Correct Option: B
Explanation:

Since the natural light is unpolarized, the first polaroid reduces the intensity to half. Therefore, percentage of incident light transmitted by first polarized is 50%

Intensity observed in an interference pattern is $I={ I } _{ 0 }\sin ^{ 2 }{ \theta  } $. At $\theta={30}^{o}$, intensity $I=5\pm 0.002$. The percentage error in angle if $I _0=20w/m^2$is

physics oscillations and waves polarization of light polarisation of light polarisation

  1. $4\sqrt { 3 } \times { 10 }^{ -2 }$%

  2. $\cfrac { 4 }{ \pi } \times { 10 }^{ -2 }$%

  3. $\cfrac { 4\sqrt { 3 } }{ \pi } \times { 10 }^{ -2 }$%

  4. $\sqrt 3\times { 10 }^{ -2 }$%

Show answer
Correct Option: C
Explanation:

$\sin\theta =\sqrt{\dfrac{I}{I _{0}}}$

Differentiating the above equation,
$\cos\theta  d\theta=\dfrac{1}{2}\dfrac{1}{I^{3/2}I _{0}^{1/2}}$
Thus $d\theta=\dfrac{1}{2I}\tan\theta dI$
$\implies \dfrac{d\theta}{\theta}=\dfrac{\tan\theta dI}{2\theta I}$

Put $\theta=30\times \dfrac{\pi}{180}radians$, $dI=0.002,I=5$,
Percentage error in angle $=\dfrac{d\theta}{\theta}\times 100$%
$=\dfrac{4\sqrt{3}}{\pi}\times 10^{-2}$%

When light passing through rotating nicol is observed, no change in intensity is seen. What inference can be drawn ?

physics oscillations and waves polarization of light polarisation of light polarisation

  1. The incident light is unpolarized.

  2. The incident light is circularly polarized.

  3. The incident light is unpolarized or circularly polarized.

  4. The incident light is unpolarized or circularly polarized or combination of both.

Show answer
Correct Option: C
Explanation:

For ordinary unpolarized light and circularly polarized light, there is no change in intensity of illumination on passing it through rotating Nicol prism.

Unpolarised light of intensity 32 W m$^{-2}$ passes through three polarizes is crossed with that of the first. The intensity of final emerging light is 3 W m$^{-2}$. The intensity of light transmitted by first polarizer will be

physics oscillations and waves polarization of light polarisation of light polarisation

  1. 32 W m$^{-2}$

  2. 16 W m$^{-2}$

  3. 8 W m$^{-2}$

  4. 4 W m$^{-2}$

Show answer
Correct Option: B
Explanation:

Intensity of polarised light transmitted from 1st polariser, 
$I _1$ = $I _0$ cos$^{2} \theta$
but (cos$^{2}\theta) _{av} = \displaystyle\frac{1}{2}$

So $I _1$ = $\displaystyle\frac{1}{2} I _0 = \frac{32}{2} = 16Wm^{-2}$

A beam of unpolarised light passes through a tourmaline crystal $A$ and then through another such crystal $B$ oriented so that the principal plane is parallel to $A$. The intensity of emergent light is $\displaystyle I$. If $A$ now rotated by $45^{o}$ in a plane perpendicular to direction of the incident ray. The emergent light will have intensity.

physics oscillations and waves polarization of light polarisation of light polarisation

  1. $\displaystyle \dfrac{I}{2}$

  2. $\displaystyle \dfrac{I}{\sqrt 2}$

  3. $\displaystyle I$

  4. $\displaystyle \dfrac{I}{4}$

Show answer
Correct Option: A
Explanation:

According to law of Malus,
$\displaystyle I = I _0 cos^{2}\theta =I _0(cos45^{o})^{2} = I _0 \left ( \frac{1}{\sqrt{2}} \right )^{2} = \frac{I _0}{2}$

Three or more number of polaroids ($n$) kept in the path of unpolarized light of intensity $I$ such that angle between any two successive polaroids is other than $90^{\circ}$, then the intensity of emergent light is :

physics oscillations and waves polarization of light polarisation of light polarisation

  1. less than I

  2. more than I

  3. I/n

  4. zero

Show answer
Correct Option: A
Explanation:

For unpolarized light, the outgoing intensity from polaroid is $I \cos ^2\theta$
Since $\cos ^2\theta \lt 1$, after passing through each polaroid the intensity will get mlultiplied by $\cos ^2\theta$ where $\theta$ is the angle between successive polaroids.
Hence, final intensity will be less than the original incident intensity.