Question

A helium–neon laser produces a beam of diameter 1.75 mm, delivering 2.25 1018 photons/s. Each photon has a wavelength of 633 nm.

(a) Calculate the amplitude of the electric field inside the beam.

_____________ kV/m

(b) Calculate the amplitude of the magnetic field inside the beam.

______________µT

(c) If the beam shines perpendicularly onto a perfectly reflecting surface, what force does it exert on the surface?

______________nN

(d) If the beam is absorbed by a block of ice at 0°C for 1.60 h, what mass of ice is melted?

______________g

Answer 1

given :

beam diameter=d=1.75 mm

number of photons per second=n=2.25*10^18 /s

wavelength of photon=lambda=633*10^(-9) m

energy of each photon=h*c/lambda

where h=planck’s constant, c=speed of light

energy=3.1403*10^(-19) J

then power=energy of one photon*number of photon per seconds

=0.70656 W

intensity=power/area

=P/(pi*(d/2)^2)

=2.9376*10^5 W/m^2

as we know, Electric field magntiude=Emax=sqrt(2*mu*c*intensity)

=sqrt(2*4*pi*10^(-7)*3*10^8*2.9376*10^5)

=1.4883*10^4 N/C

part b:

amplitude of magnetic field=amplitude of electric field/speed of light

=4.96*10^(-5) T

part c:

force=radiation pressure*area

=(intensity/speed of light)*area

=2.3552 nN

part d:

energy given to the ice block=power*time

=0.70656*1.6*3600 J

=4069.8 J

latent heat of fusion of ice=333*10^3 J/kg

so ice melted=heat transferred/latent heat of fusion of ice

=12.222 grams