Question

A laser beam of wavelength 6328 Angstrom and aperture 5 mm from He-Ne laser can be focused on an area equal to the square of its wavelength. If the laser radiates energy at the rate of 10 mW, find the angular speed of the beam and the intensity of the focused beam

Answer 1

Given that,

Wavelength = 6328 A

Aperture = 5 mm

Power = 10 mW

We need to calculate the angular velocity

Using formula of angular velocity

$\omega=\dfrac{v}{r}$

Here v = c = speed of light

Put the value into the formula

$\omega=\dfrac{3\times10^{8}}{5\times10^{-3}}$

$\omega= 6\times10^{10}\ sec$

We need to calculate the area through which the energy of beam passes

Using given statement

An area equal to the square of its wavelength.

$A=(6328\times10^{-10})^2$

$A=4\times10^{-13}\ m^2$

We need to calculate the intensity of the focused beam

Using formula of intensity

$I=\dfrac{P}{A}$

Put the value into the formula

$I=\dfrac{10\times10^{-3}}{4\times10^{-13}}$

$I=2.5\times10^{10}\ W/m^2$

Hence, The angular speed of the beam is $6\times10^{10}\ sec$

The intensity of the focused beam is $2.5\times10^{10}\ W/m^2$