Tag: oscillations and waves

Questions Related to oscillations and waves

A transparent thin plate of a polaroid is placed on another similar plate such that the angle between their axes is $30^\circ$. The intensities of the emergent and the unpolarized incident light will be in the ratio of

physics oscillations and waves polarization of light polarisation of light polarisation

  1. $1 : 4$

  2. $1 : 3$

  3. $3 : 4$

  4. $3 : 8$

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Correct Option: D
Explanation:

Let $I _0$ be the intensity of unpolarized light, then intensity of light from first transparent thin plate of a polaroid is $I=\dfrac{I _0}2$


Now this light will pass through the second similar plate whose axis is inclined at an angle of $30^o$ to that of first plate.
According to Malus law, the intensity of emerging light is:-


$I'= Icos^2 30^o=\dfrac{I _0}2\bigg(\dfrac{\sqrt 3}{2}\bigg)^2=\dfrac 38 I _0$

$\therefore \dfrac{I'}{I _0}= \dfrac 38$

Unpolarised light of intensity $32\ W\ m^{-2}$ passes through three polarizers such that transmission axis of first is crossed with third. If intensity of emerging light is $2\ W\ m^{-2}$, what is the angle of transmission axis between the first two polarisers? 

physics oscillations and waves polarization of light polarisation of light polarisation

  1. $30^{\circ}$

  2. $45^{\circ}$

  3. $22.5^{\circ}$

  4. $60^{\circ}$

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Correct Option: C
Explanation:

Let $\theta$ be angle between the axis of the first two polarisers then obviously $(90^o - \theta)$ is the angle between $2^{nd} \, and \, 3^{rd}$ polarisers. 
$\therefore I = \dfrac{I _0}{2} \, cos^2 \theta \, cos^2 (90^o - \theta)$ 

or $2 = \dfrac{32}{2} \, cos^2 \, \theta \, cos^2 \,  (90^o - \theta) = 16 cos^2 \theta \, sin^2 \theta$
$(2sin \theta \, cos \theta)^2 = \dfrac{1}{2} \, or \, sin^2 2 \theta = \dfrac{1}{\sqrt{2}}$
$\therefore 2 \theta = 45^o \, \ or \, \theta = 22.5^o$

On unpolarised beam of light is incident on a set of four polarising plates, such that each plate makes an angle of $\dfrac{\pi}{3}$ with preceding sheet. The light transmitted through the combination is:-

physics oscillations and waves polarization of light polarisation of light polarisation

  1. $\dfrac{1}{128}$

  2. $\dfrac{1}{256}$

  3. $\dfrac{1}{64}$

  4. $\dfrac{1}{32}$

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Correct Option: C

Two polaroids are kept crossed to each other. Now one of the polaroids is rotated through an angle $45^0$. The percentage of incident light now transmitted through the system is: 

physics oscillations and waves polarization of light polarisation of light polarisation

  1. 15%

  2. 25%

  3. 50%

  4. 60%

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Correct Option: B

A plane polarized light is incident normally on a tourmaline plate. Its $\vec { E } $ vectors make an angle of ${ 60 }^{ o }$ with the optic axis of the plate. Find the percentage difference between initial and final intensities.

physics oscillations and waves polarization of light polarisation of light polarisation

  1. $25$%

  2. $50$%

  3. $75$%

  4. $90$%

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Correct Option: A
Explanation:

Let the initial intensity of the light be  $I _o$.
Final intensity of the light   $I = I _o\cos^2\theta$
where  $\theta= 60^o$
$\implies \ I = I _o\times \cos^260^o = 0.25 I _o$
Percentage change in the initial and final intensities  $ = \dfrac{I _o - I}{I _o}\times 100 = \dfrac{I _o-0.25I _o}{I _o}\times 100 = 75$ %
So option C is correct.