An unpolarized beam of light is incident on a stack of ideal polarizing filters.
ID: 2015280 • Letter: A
Question
An unpolarized beam of light is incident on a stack of ideal polarizing filters. Find the fraction by which the transmitted beam's intensity is reduced in the following three cases.(a) Three filters are in the stack, each with its transmission axis at 43.7° relative to the preceding filter.
(b) Four filters are in the stack, each with its transmission axis at 30.4° relative to the preceding filter.
(c) Seven filters are in the stack, each with its axis at 16.6° relative to the proceeding filter.
Explanation / Answer
It is Known by the Malus law , we have a relation between , intensity of the incident light to transmitted light , If filter makes an angle is given by (a) I = Io cos2 where represents transmission axis makes relative to preceding filter . When , the light incident on the first filter the transmitted light intesity becomes to Half thus, I1 = Io/2 I2 = I1 cos2 I3 = I2 cos2 thus, we can simply writen as I3 = Io /2 (cos2)(cos2 ) for the fraction : I3 / Io = (cos2 )(cos2 ) /2 = (cos2 43.7 )(cos2 43.7 ) /2 = 0.136 (b) simillarly For , four filters we have , I4 / Io = (cos2 )(cos2 ) )(cos2 ) /2 = (cos2 30.4 )(cos2 30.4 ) )(cos2 30.4 ) /2 = 0.2058 (c) For , Seven filters, we have , I7 / Io = (cos2 )(cos2 ) )(cos2 ) (cos2 )(cos2 ) )(cos2 )/2 = (cos12 ) /2 = (cos12 16.6 ) /2 = 0.2999 (c) For , Seven filters, we have , I7 / Io = (cos2 )(cos2 ) )(cos2 ) (cos2 )(cos2 ) )(cos2 )/2 = (cos12 ) /2 = (cos12 16.6 ) /2 = 0.2999Related Questions
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