Question

A polarized light beam, with a 7.55 mm diameter circular cross section, is perpendicularly incident on an ideal polarizer, serving as an analyzer. The intensity of the light is 3.87 kW/m2 and the angle between the beam's polarization direction and the polarization axis of the polarizer is 19.9∘. What force in piconewtons does the light exert on the polarizer?

Answer 1

Answer:

The force is $16.727\times10^{-12}\ N$

Explanation:

Given that,

Diameter = 7.55 mm

Intensity of light = 3.87 kW/m²

Angle = 19.9°

Intensity of absorbed light

$I_{1}=E^2\sin^2\theta$

Intensity of incoming light

$I=E^2$

Ratio of intensities

$\dfrac{I_{1}}{I}=\dfrac{E^2\sin^2\theta}{E^2}$

$I_{1}=I\sin^2\theta$

Relation between intensity and power

$I_{1}=\dfrac{P}{A}$...(I)

The power is

$P=F\times c$....(II)

From equation (I) and (II)

$I_{1}=\dfrac{F\times c}{A}$

$F=\dfrac{I\sin^2\theta\times A}{c}$

Put the value into the formula

$F=\dfrac{3.87\times10^{3}\sin^2(19.9)\times\pi\times(\dfrac{7.55\times10^{-3}}{4})^2}{3\times10^{8}}$

$F=16.727\times10^{-12}\ N$

Hence, The force is $16.727\times10^{-12}\ N$