Radiance Estimate of He-Ne Laser & Tungsten Lamp

[Diemo]

Homework Statement

Estimate the radiance (in W cm^-2 sr^-1) of the following sources:
(1) A He-Ne Laser, with a beam area of 1mm², output power of 1 mW and a beam divergence of 1mrad.
(2) a 100 Watt tungsten lamp at a distance 1 m from the lamp.

Homework Equations

Well, what I have is that the luminescence is L = Phi /(Omega(A)(Cos(Theta))
Where Phi is your power emitted
A is the area of source
Omega is solidangle subtended
Theta is your angle between surface and specified direction

We also have that Omega is A/r²

The Attempt at a Solution

So, in this case we have
P=1*10^-3 W\(1*10^-3m²*1*10^-3radians)

Except that you want it is steradians, not radians, so pretty sure what I am doing there is wrong.. How would you do this?

For the second one, how do you work out what Omega is? Or what area you should be considering?

Thanks in advance.

 

[Jhero]

For the first source, the He-Ne laser, we can use the formula you provided to calculate the radiance. First, we need to convert the beam area to cm2, which gives us 0.0001 cm2. Then, we can calculate the solid angle using the formula Omega = A/r^2, where A is the area of the source and r is the distance from the source. In this case, r = 1 cm, so Omega = 0.0001 cm2/1 cm^2 = 0.0001 sr. Finally, we can plug in the values into the formula for radiance, L = Phi/(Omega*A*cos(Theta)). Since the beam divergence is given as 1 mrad, we can convert it to radians by multiplying by 0.001, which gives us 0.001 radians. So, the radiance would be L = 0.001 W cm^-2 sr^-1.

For the second source, the 100 Watt tungsten lamp, we can use the same formula. However, in this case, we need to consider the entire surface area of the lamp, which is not given. So, we can assume that the lamp has a circular shape with a diameter of 10 cm, which gives us an area of 78.5 cm2. Then, we can calculate the solid angle using the same formula as before, Omega = A/r^2, where A is now the surface area of the lamp and r is still 1 cm. So, Omega = 78.5 cm2/1 cm^2 = 78.5 sr. Finally, we can plug in the values into the formula for radiance, L = Phi/(Omega*A*cos(Theta)). Since the lamp is emitting in all directions, we can assume that the angle between the surface and specified direction is 90 degrees, so cos(Theta) = 0. So, the radiance would be L = 100 W cm^-2 sr^-1.