Focal length calculations for a double convex lens?

[arcanebop]

From what I recall, determining the focal length of a double convex lens just involves an infinite light source and holding the lens close to an image-capturing surface such as a wall and adjusting the distance until the image is at its sharpest...the distance from the lens to the surface is the focal length.

^ Correct me if I'm wrong, I want to double-check ^

What I want to know is, how does one show the calculation/determination of this, as is required by an optics project in school? Do I just draw a ray diagram for the lens, all the necessary light rays converging on a point X distance from the lens? Maybe draw it to scale?

Is that all, or is there some kind of formula that must be shown, such as the Thin Lens Equation (which doesn't make sense to me because one would have to use infinity as DO, or object distance)?

Please clarify these things for me :$

P.S. I apologize for not using the 3 guidelines to stating a question, I didn't think they applied to my question well...and I searched the forum briefly but didn't find a repeat of my question.


Thanks in advance.

 

[rollcast]

If you can measure it accurately enough or can gain the information you could use the lensmakers equation.

 

[arcanebop]

If you can measure it accurately enough or can gain the information you could use the lensmakers equation.

Hmm...I've heard of that + looked a bit into it, but it wasn't a method taught in class so I doubt it'll be accepted for the project...furthermore, I don't have measurements for the required factors of R1 and R2.

Just to clarify, I already have the focal lengths of both double convex lenses that I happen to be using for the construction of a refracting telescope. To calculate the focal length within the telescope, I simply have to subtract the eyepiece focal length from the objective focal length, is that right? In my case;

f(e) - f(o) = f(t), where f = focal length, e = eyepiece, o = objective, t = telescope
30cm-5cm=25cm ?

I think drawing a ray diagram to scale and stating the above equation satisfies the conditions of the project, but I just want to confirm that what I am doing is right. Kind of unsure if subtracting the two focal lengths is the right equation.

 

[arcanebop]

I just thought of something else, would it be a viable option to substitute the value of object distance as something radically far-off, such as 50m, which is 5000cm? Apply this to the thin lens equation for focal length for one of the lenses, and I would get almost the exact value of the actual focal length. Can I just round it to the closest whole number value, thus proving the focal length?

 

[asteriatic]

I would like to clarify that the method described in the content is a valid way to determine the focal length of a double convex lens. However, there are other methods and formulas that can also be used to calculate the focal length.

One method is to use the Thin Lens Equation, which states that 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. In this case, since the object distance is infinity, the equation simplifies to f = di. This means that the focal length is equal to the distance between the lens and the image-capturing surface where the image is at its sharpest.

Another method is to use the lensmaker's equation, which takes into account the curvature and refractive index of the lens. This equation is more complex and involves using the radii of curvature and refractive indices of the lens surfaces. However, it can provide a more accurate determination of the focal length.

In terms of showing the calculation or determination of the focal length, you can use a ray diagram to illustrate how the light rays converge at the focal point. You can also show your measurement of the distance from the lens to the image-capturing surface to verify the focal length.

In summary, there are different methods and equations that can be used to calculate the focal length of a double convex lens. It is important to understand the principles behind these methods and to choose the most appropriate one for your specific situation.