Finding the solid angle

In summary, the solid angle subtended by a 100 cm^2 circular detector at a distance of 1 m is 4∏ steradians. This can be calculated using the formula Ω = A/r^2, where A is the area of the circle and r is the distance. However, when trying to solve for r using the equation A = ∏r^2, the individual ended up with 4∏ steradians, which is the measure of a sphere. They then attempted to use the tangent to find the angle in degrees, but the correct answer is actually .01 steradians. It is important to pay attention to the meaning of the different quantities in the formulas being used.
  • #1
MickieDBaca
1
0
1. The solid angle subtended by a 100 cm^2 circular detector at a distance of 1 m is ______steradians.

2. Ω = A/r^2 and A =∏r^2 (area of a circle)

3. I originally tried to find r by solving 100 = ∏r^2 and I got r = 5.6. I then tried to plug into the first equation for Ω only to realize that really, I had just gone in a circle and ended up with 4∏, which is the measure of sphere in steradians. Then I tried the tangent (5.6/100) to find the angle in degrees... The answer is .01 but I am unsure why...
 
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  • #2
You need to keep in mind what the various quantities appearing in the formulas mean. Try again paying a bit more attention to which values go where.
 

What is a solid angle?

A solid angle is a measure of the amount of space an object takes up in three-dimensional space. It is similar to an angle in two dimensions, but instead of measuring the amount of rotation between two lines, it measures the amount of space enclosed by a cone extending from a point.

How is the solid angle calculated?

The solid angle is calculated by dividing the surface area of a portion of a sphere by the square of its radius. The resulting value is typically measured in steradians, which is the unit for solid angles. It is represented by the symbol "sr."

What is the relationship between solid angle and field of view?

The field of view is the area that can be seen by an observer or a camera. The solid angle is a measure of the size of this viewing area. As the solid angle increases, the field of view also increases, allowing for a wider view of the surrounding space.

Why is solid angle important in astronomy?

In astronomy, solid angle is used to measure the apparent size of celestial objects. This is especially useful for objects that appear to have different sizes depending on the observer's location in space. Solid angle is also used to calculate the intensity of radiation from celestial objects.

How is solid angle used in engineering and physics?

In engineering and physics, solid angle is used to calculate flux, which is the rate of flow of a physical quantity through a given surface. It is also used in optics to calculate the amount of light that passes through a given area or object, which is important in designing lenses and other optical instruments.

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