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1-Newbie

## lens

i have to plan and design an experiment to test the vadility of the hypothesis below. it is suggested that for a convergin lens the product of the object distance(u) and the image distance(v) is directly proportional to the sum of u and v, thus it obeys the equation uv=k(u+v).
how can i do this experiment?
2 REPLIES 2
On 2/11/2006 10:34:17 AM, swavez wrote:
>i have to plan and design an
>experiment to test the
>vadility of the hypothesis
>below. it is suggested that
>for a convergin lens the
>product of the object
>distance(u) and the image
>distance(v) is directly
>proportional to the sum of u
>and v, thus it obeys the
>equation uv=k(u+v).
>how can i do this experiment?
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You can use a candle for your object. Place it at the left. Cut a slit in the top of a small box and stick the lens into it so that it stands vertically above the box. You don't have to have the entire lens exposed. Carefully draw a line representing the plane of the lens and extend this line to the bottom of the box so that the position of the lens can be measured at the surface of the table/working space. Place this box near the center of your working space. Find an image box which is taller than the center of the lens. Attach a sheet of white paper to the end of the box to serve as the image screen. Now adjust the height of the candle to place the flame at the height of the center of the lens.

Your measurement pairs are the distance from the flame to the plane of the lens, and the distance from the lens to the image plane. These can be conveniently measured using the centimeter units on a yard stick, or meter stick as available.

The thin lens equation is 1/u + 1/v = 1/f. A common denominator gives (v+u)/uv = 1/f. This results in uv = f(u+v).

Plot your pairs of (u,v) measurements as y = uv and x = (u+v) This should result in a straight line whose slope is the focal length of the lens, f.

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Physics: Common Sense made Obscure by Mathematics Don Sparlin

You can test your assumptions by simply constructing a model using the lens maker formulas.

I've attached an example worksheet (Mathcad 14).  I used a system with 5 lenses, but you can mod to suit your needs.

Jack

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