Malus\' Law states that the intensity of light that emerges from two stacked pol

Question

Malus' Law states that the intensity of light that emerges from two stacked polarizers is given by I( theta ) = I0cos2( theta ), where theta is the angle between the polarization axes of the two polarizers (for example, in Figure 13.13, the angle between Polarizers I and II is 90 degree). If we let the angle between the "New" Polarizer and Polarizer I in Figure 13.13 be equal to theta, then the angle between Polarizer II and the "New" Polarizer is 90 degree - theta. Malus' Law for the case of three polarizers in a row is then I( theta ) = I0cos2(theta) cos2(90 degree - theta). Here is an opportunity for you to employ a little Mathematics to determine the orientation angle of the "New" Polarizer which yields the maximum amount of light allowed through this configuration of three polarizers: first, recall that cos(90 degree - theta ) = sin( theta ) and use the relation sin2( theta ) = l-cos2(theta ) to cast the function I( theta ) into a form that only contains powers of cos( theta ); second, determine where the function I( theta ) is a maximum by differentiating I( theta ) with respect to theta , then set dl( theta )/d theta = 0, and solve for theta , which will be the value of the angle that maximizes the intensity of light emerging from the three polarizers. Note here that you will find two different values that satisfy the equation dI( theta ) / d theta = 0, but only one of these values corresponds to the maximum of I( theta ), while the other is related to the minimum of I( theta ).

Explanation / Answer

1) I()=cos^2()*cos^2(90-)

=cos^2()*(sin^2())
= cos^2()*(1-cos^2())

2)

differentiating

dI()/d()=1/4*sin(4)

putting it zero =180/4

=45degree or 0 degree

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.