Compare the light-gathering power of the Thirty Meter Telescope with that of the dark-adapted hu

Compare the light-gathering power of the Thirty Meter...

Key Concepts

Aperture

Aperture refers to the diameter of the light-collecting element in an optical instrument, such as a telescope or even the human eye. It is a fundamental parameter in determining how much light an instrument can gather, with larger apertures capturing more photons and enabling the observation of fainter objects in the universe.

Light-Gathering Power

Light-gathering power is the measure of an optical system's ability to collect light from a source. It is directly proportional to the area of the aperture, meaning that even small increases in the diameter of the aperture result in significant enhancements in light collection, which is particularly important in astronomical observations.

Area Scaling Relationship

The area scaling relationship is a key concept in optics that notes the collecting area, and thus the light-gathering power, increases with the square of the aperture diameter. This quadratic dependency allows for a straightforward comparison between different optical systems by quantifying how enhancements in aperture size translate into improved performance, and it is essential when comparing instruments like large telescopes to the human eye.

Transcript

00:01 Question number 31 is asking us to compare the light gathering power of the 30 -meter telescope, the human eye, and one of the keck telescopes.

00:12 If you remember from the chapter, you read that the light gathering power, or lgp, as i'm going to call it, of a telescope is proportional to the area of the aperture.

00:29 I'm going to call area big a and aperture little a.

00:35 Now the area of the aperture of a telescope can be found using this formula.

00:45 Pi times d over 2 squared.

00:53 Now for each one of these we have the aperture size for each one.

01:01 The 30 meter telescope, well, that's easy to figure out.

01:05 The aperture size is within the name, 30 meters.

01:10 The human eye has an aperture size of 8 millimeters, but right off the bat, we want our units to be consistent.

01:22 We want them all in meters, so 1 millimeter is equal to 1 ,000th of a meter.

01:30 So 8 millimeters is...

01:34 Equal to 8 ,000ths of a meter.

01:39 Finally, the keck telescope has an aperture size of 10 meters.

01:49 Now, the way to figure out the area of the aperture for all of these is to just plug in those values for d and get the area of the aperture for each.

02:04 So first, let's do the 30 meters.

02:08 Telescope.

02:11 So we plug in our numbers and simplify things down.

02:19 We get 225 pi for the area of the aperture of the 30 meter telescope...

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