Question

Four polarizers are placed in succession with their axes vertical, at 30degrees to the vertical, and at 60degrees to the vertical, and at 90degrees to

Other
ANSWERED
asked 2021-04-10
Four polarizers are placed in succession with their axes vertical, at 30degrees to the vertical, and at 60degrees to the vertical, and at 90degrees to the vertical.
A. calculate what fraction of the incident unpolarizedlight is transmitted by the four polarizers.
B. Can the transmitted light be decreased by removingone of the polarizers? If so, which one?
C. Can the transmitted light intensity be extingusishedby removing one of the polarizers? If so, which one(s)?

Expert Answers (1)

2021-04-12
A) The intensity of the light passing through thesuccessive polarizers is
\(\displaystyle{I}_{{1}}={\frac{{{1}}}{{{2}}}}{I}_{{0}}\)
\(\displaystyle{I}_{{2}}={I}_{{1}}{{\cos}^{{2}}\theta_{{2}}}\)
\(\displaystyle={\frac{{{1}}}{{{2}}}}{I}_{{0}}{{\cos}^{{2}}\theta_{{2}}}\)
\(\displaystyle{I}_{{3}}={I}_{{2}}{{\cos}^{{2}}\theta_{{3}}}\)
\(\displaystyle={\frac{{{1}}}{{{2}}}}{I}_{{0}}{{\cos}^{{2}}\theta_{{2}}}{{\cos}^{{2}}\theta_{{3}}}\)
\(\displaystyle{I}_{{4}}={I}_{{3}}{{\cos}^{{2}}\theta_{{4}}}\)
\(\displaystyle={\frac{{{1}}}{{{2}}}}{I}_{{0}}{{\cos}^{{2}}\theta_{{2}}}{{\cos}^{{2}}\theta_{{3}}}{{\cos}^{{2}}\theta_{{4}}}\)
\(\displaystyle={\frac{{{1}}}{{{2}}}}{I}_{{0}}{{\cos}^{{2}}{30}}{{\cos}^{{2}}{30}}{{\cos}^{{2}}{30}}\)
\(\displaystyle={0.21}{I}_{{0}}\)
B) If we remove the second polarizer we get
\(\displaystyle{I}_{{1}}={\frac{{{1}}}{{{2}}}}{I}_{{0}}\)
\(\displaystyle{I}_{{3}}={I}_{{1}}{{\cos}^{{2}}\theta_{{3}}}\)
\(\displaystyle={\frac{{{1}}}{{{2}}}}{I}_{{0}}{{\cos}^{{2}}\theta_{{3}}}\)
\(\displaystyle{I}_{{4}}={I}_{{3}}{{\cos}^{{2}}\theta_{{4}}}\)
\(\displaystyle={\frac{{{1}}}{{{2}}}}{I}_{{0}}{{\cos}^{{2}}\theta_{{3}}}{{\cos}^{{2}}\theta_{{4}}}\)
\(\displaystyle{\frac{{{1}}}{{{2}}}}{I}_{{0}}{{\cos}^{{2}}{60}}{{\cos}^{{2}}{30}}\)
\(\displaystyle={0.094}{I}_{{0}}\)
Thus we can decrease the intensity byremoving the second or third polarizer.
C) If we remove the second and thirdpolarizers we will have two polarizers with their axesperpendicular to each other and so no light willbe transmitted.
17
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-03-10
Four polarizers are placed in succession with their axesvertical, at 30 degrees to the vertical, and at 60 degrees to thevertical, and at 90degrees to the vertical.
A. calculate what fraction of the incident unpolarizedlight is transmitted by the four polarizers.
B. Can the transmitted light be decreased by removingone of the polarizers? If so, which one?
C. Can the transmitted light intensity be extingusishedby removing one of the polarizers? If so, which one(s)?
asked 2021-04-02
A beam of light passes through a polarizer and then ananalyzer. In this process, the intensity of the lighttransmitted is reduced to 10% of the intensity incident on theanalyzer. What is the angle between the axes of the polarizerand the analyzer?
asked 2021-02-10
Two light sources of identical strength are placed 8 m apart. An object is to be placed at a point P on a line ? parallel to the line joining the light sources and at a distance d meters from it (see the figure). We want to locate P on ? so that the intensity of illumination is minimized. We need to use the fact that the intensity of illumination for a single source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source.
asked 2021-05-03
A charge of \(\displaystyle{6.00}\times{10}^{{-{9}}}\) C and a charge of \(\displaystyle-{3.00}\times{10}^{{-{9}}}\) C are separated by a distance of 60.0 cm. Find the position at which a third charge, of \(\displaystyle{12.0}\times{10}^{{-{9}}}\) C, can be placed so that the net electrostatic force on it is zero.
...