CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A plane wave of intensity I=0.70 W cm2 illuminates a sphere with ideal mirror surface. The radius of sphere is R=5.0 cm. From the standpoint of photon theory, find the force that light exerts on the sphere (in μN).

Open in App
Solution

Imagine the sphere to be made of thin circular rings of radius r, thickness ds=R dθ and subtending an angle of θ at the center.




Since, surface of mirror is considered to be ideal, i.e., reflection coefficient is unity, photons suffer momentum change in normal direction only.
Along normal momentum per second of incident photons,
(dPdt)incident=IcdA cos2θ
Due to collision rate of change of momentum of photons is
(dPdt)photon=2IcdA cos2θ
Force experienced by the ring along normal is
dFn=(dPdt)ball=+2IcdA cos2θ
This force may be resolved into horizontal and vertical components.
The vertical component dFnsinθ is cancelled because every element on the upper half has a symmetrically placed element in the lower half.
So, resultant force on the ball is
F=dFncos θ=2IcdA cos3θ
dA=(2πR sin θ)R dθ
F=π204IcR2cos3θ sin θdθ
F=4πR2Icπ20cos3θsin θ dθ=πR2Ic
On substituting values,
F=π×25×104(0.70×1043×108)N
F=0.18 μN.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Intensity in Photon Model
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon