When the light is incident from either the left or the right,the transmitted int

Question

When the light is incident from either the left or the right,the transmitted intensity is one-half the incident intensity. When the light is incident from either the left or the right,the transmitted intensity is one-fourth the incidentintensity. When the light is incident from the left, the transmittedintensity is one-half the incident intensity; when the light isincident from the right, the transmitted intensity is zero. When the light is incident from the left, the transmittedintensity is one-fourth the incident intensity; when the light isincident from the right, the transmitted intensity is one-half theincident intensity. When the light is incident from the left, the transmittedintensity is one-half the incident intensity; when the light isincident from the right, the transmitted intensity is one-fourththe incident intensity. 0.   The drawing shows two sheets of polarizing material. Polarizer1 has its transmission axis aligned vertically, and polarizer 2 hasits transmission axis aligned at an angle of 45° with respectto the vertical. Light that is completely polarized along thevertical direction is incident either from the far left or from thefar right. In either case, the average intensity of the incidentlight is the same. Which one of the following statements is trueconcerning the average intensity of the light that is transmittedby the pair of sheets?
(a)   When the light is incident from either the left or the right,the transmitted intensity is one-half the incident intensity. (b)   When the light is incident from either the left or the right,the transmitted intensity is one-fourth the incidentintensity. (c)   When the light is incident from the left, the transmittedintensity is one-half the incident intensity; when the light isincident from the right, the transmitted intensity is zero. (d)   When the light is incident from the left, the transmittedintensity is one-fourth the incident intensity; when the light isincident from the right, the transmitted intensity is one-half theincident intensity. (e)   When the light is incident from the left, the transmittedintensity is one-half the incident intensity; when the light isincident from the right, the transmitted intensity is one-fourththe incident intensity.

Explanation / Answer

Light incident from left :
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Intensity of the light after 1 st polariser I ' =I   where I = intensity of the incident light Intensity of the light after 2 nd polariser I " = I ' cos2 ( 45 )   Since from malus law                                                                = 0.5 I ' = 0.5 I                                                                = I / 2 Light incident from right :
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Intensity of the light after 1 st polariser I ' =I cos 2 45 where I = intensity of the incident light I ' = 0.5 I Intensity of the light after 2 nd polariser I " = I ' cos2 ( 90- 45 )   Since from malus law                                                                = 0.5 I ' = 0.25 I                                                                = I / 4 Therefore answer is option ( e) i.e., When the light is incident from the left, thetransmitted intensity is one-half the incident intensity; when thelight is incident from the right, the transmitted intensity isone-fourth the incident intensity. Light incident from right :
------------------------
Intensity of the light after 1 st polariser I ' =I cos 2 45 where I = intensity of the incident light I ' = 0.5 I Intensity of the light after 2 nd polariser I " = I ' cos2 ( 90- 45 )   Since from malus law                                                                = 0.5 I ' = 0.25 I                                                                = I / 4 Therefore answer is option ( e) i.e., When the light is incident from the left, thetransmitted intensity is one-half the incident intensity; when thelight is incident from the right, the transmitted intensity isone-fourth the incident intensity.

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