# Focal length calculation and graph Q

by _Greg_
Tags: calculation, focal, graph, length
 P: 38 Hi folks, just joined the forums Hope you dont mind me firing a few questions now and again, i have some reports to do over the weekend which is the last of my HNC in Chemical Engineering A lot of it is basic physics which iv done in the past but its just the odd bit that catches me out. So anyway, iv done an expeiment with a converging lens where you alter the object distance and image distance ( U & V ) to get focused images on the screen. With these results iv plotted a graph of V against U which produces a curved slope (diagram 1) Then i done a graph of 1/V and 1/U which produces a straight line which intercepts the x and y axis, these values being 1/f (diagram 2) My question is Why is the graph of U and V not useful for finding the focal length of the lens accurately? probably an easy question but i just cant put my finger on it cheers
 P: 92 use similar triangles to proove that the formula for a lens is (1/U + 1/V = 1/f) or u can find it anywhere on the internet. it is a very easy proof, won't take you 5 min. therefore it is 1/U and 1/V not U and V
 P: 38 not entirly sure what you mean, triangles? anyway, that 1/V vs 1/U graph with my experimental results is proof that the equation is true. im just asked why the U and V graph doesnt give an accurate value for the focal length?
P: 92

## Focal length calculation and graph Q

ok

if you draw your object, lens and image on a piece of paper with two of the rays you use to draw a ray diagram, you can see that there are some similar triangles on that figure. Try using similar triangles and getting two equations involving U, V and f.

then solve them simultaneously to get "1/U + 1/V = 1/f "

(if you cannot I can give you the solution but try it first :)

U and V graph cannot give you an accurate value for the focal length because the relation between the two is not related to f in any simple way.
if u play around with the equation I gave you above you might get " "[(v+U)/U]*f=V" but this won't make it any easier.

perhaps the answer to your question is that the nature of lenses does not provide us with that simple relations where you plot U versus V and get a slope or a y intercept of f

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