How could you find the focal length of a convex lens: a)rapidly but approximately, and b) accurately?

Question

a 'ray diagram' and the common 'equation: 1/u + 1/v = 1/f ' are two answers but i don't know where they fit in.

Answer 1

best way is to take the radius of curvature of the lens.

This is just the radius of a circle which would be made if the curve of a lens was extended to make such a shape.

1/2 radius = focal length

To hell with ray diagrams... Way too much work.

Answer 2

Put a paper and put the lens in front of it and capture the image of a distant object by moving the lens to and fro. When a sharp and inverted image is formed, measure the distance between the lens and the paper. That is a rapid and approximate method of measuring the focal length of the lens. Since u the distance from the object to the lens is large, 1/u can be neglected and that equation can be written as 1/v = 1/f and thus v = f

Accurate determination involves more precise measurements and ensuring that the incoming rays are parallel. Image of the sun and stars is a good way ensuring that the incoming rays are parallel.

Answer 3

You can do as one respondent suggests and focus the sun to a point, in practice this tends to not work very well since the focal point of the sun is so bright it saturates your retina quickly and you can't see when it is in focus.

A perhaps more practical crude estimate of the focal length of a convex lens can be made, assuming the focal length is not huge, say order of 500 mm or smaller, by putting a table lamp across a room from you and casting the image of the light bulb on the wall. The image will be in focus at nearly the focal length of the lens and it should be very much smaller than the light bulb itself.

An accurate method would be to find the point where the light bulb image is exactly the same size as the light bulb itself, at that point both the image and the bulb are at twice the focal length.

You can estimate the errors in the crude method using your formula above.

Answer 4

The easy and accurate way is to focus the suns rays to a spot and measure the distance from lens to spot.

Answer 5

a) as per answerer 1

b) I would imagine the lens equation, make f the subject of that equation and measure u and v