Converging lens magnification

In summary, the equation q=(1+m)f is a general equation derived from the thin-lens and magnification equations, assuming a non-negative convention for the magnification equation. However, there may be a problem with the question as stated.
  • #1
ben488
2
0
If I have a converging lens, of focal length f, and magnification of the image m, where q is the distance of the image from the lens show that q = (1+m) f

m = - q/p
1/f = 1/p + 1/q


I just need to show that they are equal, but I am getting confused with the maths..

q= (1 - (q/p)) (1/(1/p + 1/q))
q= (1 - (q/p))(qp/(p+q)
q= (qp/p + q) - (q/p)(qp/(p+ q)
 
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  • #2
If by "they" you mean p=q, you could look at the scene from the ray diagram point of view. The only situation where p=q for a converging lens, is when both are at a point at 2x the focal length of the lens. At this point, the gemoetry is perfectly symmetrical, and image is the same size as the object, therefore, magnification is 1 (w
 
  • #3
ben488 said:
I just need to show that they are equal, but I am getting confused with the maths..

q= (1 - (q/p)) (1/(1/p + 1/q))
q= (1 - (q/p))(qp/(p+q)
Good. Rearranging, this becomes:
q= [(p-q)/p][qp/(p+q)] = [(p-q)/(p+q)]q

Well, looks like it's not true! :eek:

Perhaps they meant to write: q = (1-m)f
 
  • #4
Actually I get unity each time I do it (actually 1= -1). So then I noticed that the first equation:
q= (1+m)f
is derived directly from the thin-lens and magnification equations, if you use m=q/p (no negative).

So the equation q=(1+m)f is a general equation (true for all real situations) not a specific equation, as long as you are using the non-negative convention for the magnification equation.

There is a problem with the question, as stated.
 
  • #5
thanks so much for all your help, its great.

Ben
 

1. What is a converging lens?

A converging lens is a type of lens that is thicker in the middle and thinner at the edges, causing light rays to converge or come together. It is also known as a convex lens.

2. How does a converging lens magnify objects?

A converging lens magnifies objects by bending light rays as they pass through the lens, causing the image of the object to appear larger. The amount of magnification depends on the focal length of the lens.

3. What is the formula for calculating magnification of a converging lens?

The formula for calculating magnification of a converging lens is M = -v/u, where M is the magnification, v is the distance of the image from the lens, and u is the distance of the object from the lens.

4. Can a converging lens produce both real and virtual images?

Yes, a converging lens can produce both real and virtual images depending on the position of the object relative to the focal point of the lens. If the object is placed beyond the focal point, a real image will be produced. If the object is placed between the lens and the focal point, a virtual image will be produced.

5. How does the distance between the object and the lens affect the magnification?

The distance between the object and the lens affects the magnification because the closer the object is to the lens, the larger the magnification will be. This is because a shorter distance between the object and the lens will result in a larger angle of convergence, causing the image to appear larger.

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