Question

In Fig. 33-29, unpolarized light is sent into a system of five polarizing sheets. Their polarizing directions, measured counterclockwise from the positive direction of the y axis, are the following: sheet 1,$\mathbf{35}\mathbf{°}$; sheet 2, $\mathbf{0}\mathbf{°}$; sheet 3,$\mathbf{0}\mathbf{°}$; sheet 4,$\mathbf{110}\mathbf{°}$; sheet 5,$\mathbf{45}\mathbf{°}$. Sheet 3 is then rotated$\mathbf{180}\mathbf{°}$,counterclockwise about the light ray. During that rotation, at what angles (measured counterclockwise from the y axis) is the transmission of light through the system eliminated?

Short answer

At angles $20°\mathrm{and}90°$, the transmission of light through the system gets eliminated.

Step-by-step solution

The given data

Polarizing angles of five sheets are given:

Sheet 1-$35°$

Sheet 2-$0°$

Sheet 3-$0°$

Sheet 4-$45°$

Sheet 5-$180°$

Understanding the concept of polarizing angle

The polarizing angle is the angle at which the unpolarized light or other electromagnetic radiation must be incident upon a nonmetallic surface for the reflected radiation to acquire maximum plane polarization. Here, we need to use the concept of polarization of light using polarizing sheets. The transmission of light can be eliminated only if the polarizing directions of immediate sheets become perpendicular to each other. So, when rotating polarizing sheet 3, we need to check at which angle the polarization direction of sheet 3 will get crossed with sheet 2 or sheet 4.

Calculation of the angles of lights at which the transmission of light is eliminated

We have the polarization direction of sheet 4 at $110°$counterclockwise from the y-axis. So, when we rotate the polarizing direction of sheet 3 counterclockwise from the y-axis, it becomes perpendicular to the polarizing direction of sheet 4.

Thus, at $20°,$the transmission of light through the system is eliminated.

When we further rotate sheet 3 and come at an angle $90°,$ the polarization direction of sheet 3 becomes perpendicular to sheet 2 because we know that the polarization direction of sheet 2 is along the y-axis $\left(0°\right)$.

From $90°\text{to}180°$, there is no possibility of polarization direction getting crossed with each other.

Hence, we can conclude that during rotation at angles $20°\text{and}90°$the transmission of light through the system gets eliminated.