Examine Figure 81.7 B. The map in the figure is 360^∘ wide and 180^∘ tall. An angle of 1^∘ on th

Examine Figure 81.7 B. The map in the figure is 360^∘ wide...

Key Concepts

Angular Size and Distance Conversion

This concept involves converting an observed angular measurement (in degrees) into a physical size using a distance scale factor. In astronomy, knowing how many kiloparsecs (kpc) correspond to a given angle on the sky is critical for determining the size of astronomical objects or regions when their distance is known. It underlies the method of inferring the linear dimensions from the apparent angular sizes in maps or images of the sky.

Cosmic Expansion and Scale Factor

This concept pertains to how the sizes of structures evolve over time due to the expansion of the universe. The scale factor relates the dimensions of an object or region in the early universe to its present-day size, reflecting how distances between objects inflate with cosmic expansion. It is essential in cosmology for comparing structures from different epochs in the history of the universe.

Large-Scale Structure of the Universe

This refers to the organization of matter on the largest scales, including clusters of galaxies, filamentary networks, and voids. Understanding the sizes, distributions, and evolution of high-density regions in the early universe provides insights into the formation and evolution of the cosmic web observed today. It connects observational data from early epochs with current models of galaxy formation and cosmological structure.

Transcript

00:03 So this question here is asking about our ability to draw a ray diagram for a thin lens.

00:13 And so we're going to set up the system.

00:19 The lens kind of is shown in the diagram here.

00:22 I'll use a little ruler and i'm going to use for the for the scale.

00:29 I'm going to use that every basically half a centimeter on my ruler is going to be represented a centimeter on the diagram.

00:40 So if i start here, let us say at that point, then we know that the focal point is 15 centimeters from there.

00:54 So i use a half centimeter for every centimeter.

00:56 So that's one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen right here.

01:09 That's where it would be.

01:10 Ok, and then the other side focal point is going to be one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen.

01:31 So it's going to be over there.

01:33 And then the object is going to be seven centimeters.

01:37 That's one, two, three, four, five, six, seven.

01:41 That's going to be right there.

01:45 And so if we just move this away, mark that point right there.

01:57 And we also need to draw the size of the object.

02:02 It says it's five centimeters tall.

02:04 So i'll just right here where that's where the object is supposed to be.

02:08 I'm just going to do a five centimeter tall object, which is to this scale here.

02:17 It's going to be one, two, three, four, five.

02:25 And that's where my object is going to be.

02:27 Ok, so now we need to draw a line representing the lens, the center line of the lens.

02:34 Because we need to use that.

02:36 We're trying to get fairly accurate drawing here.

02:42 Let's just move it down just a tad.

02:47 There we go.

02:49 And so now we can use, draw a dotted line here, represent the center line of our lens.

03:00 So now we're ready to start drawing some rays that we can trace.

03:05 First, we know that a ray of light that goes into my lens parallel to the principal axis.

03:12 So that would be this one with a ruler drawn with a zero degree marking on it.

03:16 We know that it's going to go in parallel to the principal axis.

03:23 That would be this one.

03:25 It should refract out through the focal point on the other side of the lens.

03:43 So that would be this line.

03:48 There's one of my rays.

03:53 And we know that a ray of light that goes in along the line containing a focal point on this side.

04:06 So that would be like this.

04:08 You can't go in from the object to the focal point and then go into the lens because the object is located within the focal length of the lens.

04:17 But we can do it along this line.

04:18 We can say that a light ray that is along this line and goes into my lens should refract out parallel to the principal axis.

04:29 This.

04:36 And finally, a ray of light that goes in to my lens through the center of the lens itself should not be refracted.

04:47 It should just kind of keep going.

04:50 So that would be this one...

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