Solving for p: Finding Distance from Convex Lens

In summary, to find p, the distance of the object from the convex lens, given only the distance between the object and its image (p + q), you can use the formula 1/p + 1/q = 1/f, where f is the focal length of the lens. Additionally, knowing that the image is smaller than the original by a factor of 1/2 can help determine p and q using similar triangles or the formula for object and image heights.
  • #1
Nano
34
0

Homework Statement


Given only the distance between the object and its image (p +q), how is it possible to find p, the distance of the object from the convex lens?


Homework Equations


1/p + 1/q = 1/f
in this case, p + q =40
also, the image is smaller than the original, so p > 2f


The Attempt at a Solution


I don't understand how to find p if q and f are unknown. I tried solving for q as q=40-p, but that didn't take me anywhere.
 
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  • #2
You need more information than you gave in part 1.
How did you know the image is smaller than the original - do you know what fraction it is?
 
  • #3
It said if was 1/2 the size of the original. But how does that information help?
 
  • #4
Ahh, I think I get it. It has something to do with the similar triangles formed by the object/image and a light ray passing through the center of the convex lens, right?
 
  • #5
Yes, or you can use the formula relating the object and image heights to their distances from the lens to get a 2nd equation relating p and q.
 
  • #6
Ok, thank you for your help!
 

1. What is the formula for finding the distance from a convex lens?

The formula for finding the distance (p) from a convex lens is 1/f = 1/p + 1/q, where f is the focal length of the lens and q is the distance of the image from the lens.

2. How does the distance from the object affect the image formed by a convex lens?

The distance from the object (p) directly affects the distance of the image (q) from the lens. As p increases, q decreases and vice versa. This is because the convex lens follows the inverse relationship between p and q described by the formula 1/f = 1/p + 1/q.

3. Can a convex lens form both real and virtual images?

Yes, a convex lens can form both real and virtual images depending on the placement of the object and the distance of the image. When the object is placed further than the focal length from the lens, a real image is formed. When the object is placed closer than the focal length, a virtual image is formed.

4. How do I know if the image formed by a convex lens is upright or inverted?

The orientation of the image formed by a convex lens depends on the placement of the object. If the object is placed beyond the focal length, the image will be inverted. If the object is placed between the lens and the focal length, the image will be upright.

5. Can a convex lens form a magnified image?

Yes, a convex lens can form a magnified image if the object is placed between the lens and the focal length. The magnification depends on the ratio of the distances between the object and the lens and the image and the lens.

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