Problem on thermal radiation and lenses

AI Thread Summary
The discussion revolves around calculating the diameter of an image formed by a lens when observing the Sun, which is assumed to produce parallel rays due to its great distance. The concept of "angular diameter" is introduced, defined as the angle subtended at the observer, which is crucial for understanding how the image size relates to the object size. The lens diameter of 100mm is relevant because it affects the amount of light captured and the resolution of the image formed. Despite light rays converging at a focal point, the image retains a measurable diameter due to the angular relationship between the object and the lens. Clarifying these concepts helps resolve confusion regarding the image formation process.
phantomvommand
Messages
287
Reaction score
39
Homework Statement
Please see the attached photo
Relevant Equations
P (rad) = sigma e0 T^4
At long distances, images due to convex lenses are formed at the foci.
Screenshot 2021-03-13 at 2.32.22 PM.png

I know that the Sun is at a very far distance from the lens, so I assume the rays are parallel and the image is formed at the focus (500mm away from the centre of the lens).
How do I calculate the diameter of the image?
The hint to solving this problem says that "The angular diameters of object and image are equal". What is the "angular diameter", and what does the hint mean? If the light rays intersect at a focal point, how can there even be a diameter? Furthermore, how is the fact that the lens diameter = 100mm useful?

I am quite confused by this question, any help is appreciated. Thank you!
 
Physics news on Phys.org
phantomvommand said:
Homework Statement:: Please see the attached photo
Relevant Equations:: P (rad) = sigma e0 T^4
At long distances, images due to convex lenses are formed at the foci.

View attachment 279679
I know that the Sun is at a very far distance from the lens, so I assume the rays are parallel and the image is formed at the focus (500mm away from the centre of the lens).
How do I calculate the diameter of the image?
The hint to solving this problem says that "The angular diameters of object and image are equal". What is the "angular diameter", and what does the hint mean? If the light rays intersect at a focal point, how can there even be a diameter? Furthermore, how is the fact that the lens diameter = 100mm useful?

I am quite confused by this question, any help is appreciated. Thank you!
A ray arriving from a point at one edge of the sun, as observed from Earth, is not quite parallel with a ray from the opposite edge, so they will not focus at the same point.
OTOH, rays from one point on the sun arriving at different points of the lens are effectively parallel, so do focus at the same point.
As a result, an actual image of the sun is produced, spots and all.
 
haruspex said:
A ray arriving from a point at one edge of the sun, as observed from Earth, is not quite parallel with a ray from the opposite edge, so they will not focus at the same point.
OTOH, rays from one point on the sun arriving at different points of the lens are effectively parallel, so do focus at the same point.
As a result, an actual image of the sun is produced, spots and all.
Thanks for the reply. Could you please explain what angular diameter is about?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
Thread 'Voltmeter readings for this circuit with switches'
TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
Thread 'Trying to understand the logic behind adding vectors with an angle between them'
My initial calculation was to subtract V1 from V2 to show that from the perspective of the second aircraft the first one is -300km/h. So i checked with ChatGPT and it said I cant just subtract them because I have an angle between them. So I dont understand the reasoning of it. Like why should a velocity be dependent on an angle? I was thinking about how it would look like if the planes where parallel to each other, and then how it look like if one is turning away and I dont see it. Since...
Back
Top