The size of the image of the Sun

In summary, the focal length of a concave mirror is given as f=20 cm, and the mirror is directed towards the sun at an angle of 1° at the pole. Using the equation 1/u + 1/v = 1/f and assuming the light comes from a very large distance (u=∞), we can find that the image of the sun is located at v=20 cm. However, in terms of angles, the angular magnification is zero as the distance and size of the sun are effectively infinite. Instead, we can look at the ratio of angles and see that the sun subtends an angle of 1° on Earth when u and l1 are very large.
  • #1
Akash47
53
5

Homework Statement


The focal length of a concave mirror is f=20 cm. It is directed towards the sun and the sun makes an angle= 1° at the pole of the mirror. What is the size of the image of the sun?

Homework Equations


1/u +1/v =1/f ...(i) ,magnification= v/u= l2/l1 where l1 =size of the sun,l2 =size of image of the sun.

The Attempt at a Solution


Here,u=∞(as the light comes from a very large distance),so from (i),v= f =20 cm.So v/u= 20/∞ =0=l2 /l1,from that, l2=0 or l1=∞.But which is right?Also I can't make a relation with the given angle.This is all what I have done.Please point out the mistake in my approach and also give hints to carry it out.
 
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  • #2
Akash47 said:
magnification= v/u
This is not useful here. Just as the distance to the sun is effectively infinite, so is its size, so the magnification in this sense is zero. You need instead to look at the ratio of the angles (angular magnification).
Instead of saying the sun is at infinity, just let u and l1 be very large. In terms of those, what angle does the sun subtend on Earth?
 

Related to The size of the image of the Sun

1. What is the size of the image of the Sun?

The size of the image of the Sun can vary depending on the instrument used to capture it. However, on average, the image of the Sun is about 1.39 million kilometers in diameter.

2. How do scientists measure the size of the image of the Sun?

Scientists use specialized instruments, such as telescopes and cameras, to capture images of the Sun. They then use mathematical techniques to calculate the size of the image based on the resolution and distance of the instrument.

3. Does the size of the image of the Sun change over time?

Yes, the size of the image of the Sun can change slightly over time due to its complex and dynamic nature. Solar flares, prominences, and other solar activity can cause slight variations in the size of the image.

4. How does the size of the image of the Sun compare to other stars?

The Sun is considered a medium-sized star, with a diameter that is about 109 times that of Earth. In comparison, there are stars that are much larger and smaller than the Sun, with some being hundreds of times larger.

5. How has our understanding of the size of the image of the Sun evolved over time?

Our understanding of the size of the image of the Sun has evolved greatly over time. Ancient civilizations believed the Sun to be much smaller than it actually is, while modern technology and scientific advancements have allowed us to accurately measure and study the Sun's size and structure.

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