Focal length equation from Radii of Curvature and refractive index of lens

In summary, the conversation is about finding an equation for the focal length of a biconvex lens, taking into account the radii of curvature, thickness, and refractive index inside and outside the lens. The equation is mentioned on Wikipedia, but the person needs a legitimate source and a more general version of the equation. They ask for help finding a derivation or direction for further research. The person later updates that they have found what they were looking for through additional searching and provides a link to a source. They mention that this equation can be found in an optics textbook.
  • #1
Snoopey
6
0
Hi all,

I'm looking for an equation which will give me the focal length of a biconvex lens given that we know both Radii of curvature, the thickness of the lens and the refractive index inside and outside.

An equation is given on wikipedia here http://en.wikipedia.org/wiki/Focal_length as

d5d9b5b95cf3fd9ea7f2549ae4ee8fa6.png


I need something I can reference though and I can't see this equation anywhere else I look. Also I need a more general version of the equation which involves the refractive index of the substance surrounding the lens.
Could anyone point me to a derivation of this formula or lead me in the right direction?

I also need to find a legitimate source for the back focal distance shown on the same page of wikipedia:

30eebfeda11493b69809a64439377125.png


Thanks all!

EDIT: Found what I was looking for, just needed a bit more snooping!
http://physics.tamuk.edu/~suson/html/4323/thick.html
 
Last edited:
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  • #2
Any decent optics textbook (e.g. Hecht) should have that equation, in a chapter on thick lenses.
 

1. What is the focal length equation from radii of curvature and refractive index of a lens?

The focal length equation from radii of curvature and refractive index of a lens is given by f = (n-1)(1/R1 - 1/R2), where n is the refractive index of the lens, R1 is the radius of curvature of the first surface of the lens, and R2 is the radius of curvature of the second surface of the lens.

2. How is the focal length of a lens affected by the refractive index?

The focal length of a lens is directly proportional to the refractive index of the lens. This means that as the refractive index increases, the focal length also increases. This relationship is represented by the focal length equation from radii of curvature and refractive index.

3. Can the focal length equation be used for all types of lenses?

Yes, the focal length equation from radii of curvature and refractive index can be used for all types of lenses, including convex, concave, and even complex lenses with multiple surfaces. However, it is important to note that this equation is an approximation and may not be accurate for lenses with very high refractive indices or extreme curvatures.

4. What does the focal length of a lens tell us?

The focal length of a lens is a measure of its ability to bend light rays. It is the distance between the lens and its focal point, where parallel light rays converge after passing through the lens. A shorter focal length means a stronger bending of light rays, which results in a more magnified image.

5. How can the focal length equation be used in practical applications?

The focal length equation from radii of curvature and refractive index is commonly used in the design and manufacturing of lenses, such as in cameras, telescopes, and eyeglasses. It allows engineers and scientists to calculate the necessary parameters for a desired focal length, which is crucial in achieving the desired magnification and image quality.

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