Wave Optics - Size of Illuminated spot on a screen

[Keano16]

Homework Statement

A convex lens has a radius of 20mm and a focal length of 100mm. A point source of light is placed 500mm behind the lens and a screen is placed 120mm in front of it. Calculate (to first order) the size of the illuminated spot on the screen. Now calculate the distance at which the screen should be placed to get the best possible image, and estimate the spot size in this case.

Homework Equations

The Attempt at a Solution

I can picture what is physically going on in this situation, and I think that the reason as to why this is occurring is aberration due to the lens.

I'm not sure how I am meant to estimate the size of the spot though -- in what terms etc.

Would love any pointers.

 

[anathema]

Thank you for your post. I can help you with your question. To estimate the size of the illuminated spot on the screen, we can use the thin lens equation:

1/f = 1/v + 1/u

where f is the focal length, v is the distance from the lens to the image, and u is the distance from the lens to the object. In this case, we have f = 100mm, u = 500mm, and v = 120mm. Solving for v, we get v = 109.09mm. This means that the image of the point source will be 109.09mm away from the lens, and the size of the spot on the screen will be approximately 109.09mm/500mm = 0.218mm.

To find the distance at which the screen should be placed to get the best possible image, we can use the formula for magnification:

M = -v/u

where M is the magnification, v is the distance from the lens to the image, and u is the distance from the lens to the object. In this case, we want the magnification to be as close to 1 as possible, so we want v to be equal to u. This means that the screen should be placed at a distance of 500mm from the lens to get the best possible image. At this distance, the spot size on the screen will be approximately 0.2mm.

I hope this helps. Let me know if you have any further questions or need clarification. Good luck with your research!