# Radiance Estimate of He-Ne Laser & Tungsten Lamp

• Diemo
In summary, for the first source, the He-Ne laser, the radiance is 0.001 W cm^-2 sr^-1. For the second source, the 100 Watt tungsten lamp, the radiance is 100 W cm^-2 sr^-1.
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

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?

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.

## 1. What is a radiance estimate of a laser or lamp?

A radiance estimate is a measurement of the amount of light emitted from a laser or lamp, typically expressed in watts per square meter per steradian (W/m2/sr). It takes into account both the intensity and angular distribution of the light.

## 2. How is the radiance estimate of a laser or lamp calculated?

The radiance estimate is calculated by dividing the total radiant flux (measured in watts) by the solid angle (measured in steradians) and the surface area (measured in square meters) of the emitting source.

## 3. What is the difference between the radiance estimate of a He-Ne laser and a Tungsten lamp?

The main difference between the radiance estimates of a He-Ne laser and a Tungsten lamp is the spectral distribution of the emitted light. He-Ne lasers emit a single wavelength of light (632.8 nanometers), while Tungsten lamps emit a broad spectrum of wavelengths. Additionally, the radiance estimate of a He-Ne laser is typically much higher than that of a Tungsten lamp.

## 4. Why is it important to measure the radiance estimate of a laser or lamp?

Measuring the radiance estimate of a laser or lamp is important for several reasons. It allows us to quantify the amount of light emitted, which is useful for applications such as lighting design and laser safety. It also helps us understand the performance and efficiency of the emitting source, which can inform improvements in technology and design.

## 5. How does the radiance estimate of a laser or lamp affect its practical use?

The radiance estimate of a laser or lamp can have a significant impact on its practical use. For example, a higher radiance estimate means that the light is more concentrated and can travel longer distances without significant loss. This is important for applications such as telecommunications and laser cutting. On the other hand, a lower radiance estimate may be more suitable for applications that require a broader, less intense distribution of light, such as photography or general lighting.

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