Answer:
The force is [tex]16.727\times10^{-12}\ N[/tex]
Explanation:
Given that,
Diameter = 7.55 mm
Intensity of light = 3.87 kW/m²
Angle = 19.9°
Intensity of absorbed light
[tex]I_{1}=E^2\sin^2\theta[/tex]
Intensity of incoming light
[tex]I=E^2[/tex]
Ratio of intensities
[tex]\dfrac{I_{1}}{I}=\dfrac{E^2\sin^2\theta}{E^2}[/tex]
[tex]I_{1}=I\sin^2\theta[/tex]
Relation between intensity and power
[tex]I_{1}=\dfrac{P}{A}[/tex]...(I)
The power is
[tex]P=F\times c[/tex]....(II)
From equation (I) and (II)
[tex]I_{1}=\dfrac{F\times c}{A}[/tex]
[tex]F=\dfrac{I\sin^2\theta\times A}{c}[/tex]
Put the value into the formula
[tex]F=\dfrac{3.87\times10^{3}\sin^2(19.9)\times\pi\times(\dfrac{7.55\times10^{-3}}{4})^2}{3\times10^{8}}[/tex]
[tex]F=16.727\times10^{-12}\ N[/tex]
Hence, The force is [tex]16.727\times10^{-12}\ N[/tex]
