Effective Focal Length of Multiple Lenses

In summary, the author discusses how a multiple lens system can be simplified by considering it as a single lens system with an effective focal length. The formula for the effective focal length is 1/f(effective) = 1/f1 + 1/f2 + ... + 1/fn. The position of the resulting "effective" lens is well-defined for thin lenses in contact with each other, but not for a simple two lens system.
  • #1
RWard29
2
0
In my Optics book (Hecht, 4th edition) the author discusses how, when dealing with a multiple lens system (say, with n many lenses), one can think of the system as a single lens system, with an effective focal length given by:

1/f(effective) = 1/f1 + 1/f2 + ... + 1/fn

My question is this: Where is the resulting "effective" lens located, with respect to the original source (or with respect to the original lenses)? I am dealing with a simple two lens system, and I've tried placing the lens at the midpoint between the original two, and at the location of lens 1, but neither gives the correct answer.
 
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  • #2
Nevermind. I just answered my own question; I read what I wanted to see, not what was actually there. The formula I quoted applies only to thin lenses which are in contact with each-other, in which case the position of said "effective" lens is already well-defined.
 

FAQ: Effective Focal Length of Multiple Lenses

1. What is the effective focal length of multiple lenses?

The effective focal length of multiple lenses is the combined focal length of the lenses when used together. It takes into account the magnifying power of each individual lens and how they work together to create a final image.

2. How is the effective focal length of multiple lenses calculated?

The effective focal length is calculated by multiplying the focal lengths of each lens and dividing by the total distance between the lenses. This formula is known as the lens combination formula and is represented as 1/f = 1/f1 + 1/f2 + ... + 1/fn, where f is the effective focal length and fn is the focal length of each individual lens.

3. Can the effective focal length be greater than the individual focal lengths?

Yes, the effective focal length can be greater than the individual focal lengths. This is because when lenses are placed close together, they create a magnifying effect that increases the overall focal length. This is known as the combined focal length or power of lenses.

4. How do different types of lenses affect the effective focal length?

The type of lens used will affect the effective focal length. Convex lenses (converging lenses) have a positive focal length and will increase the effective focal length, while concave lenses (diverging lenses) have a negative focal length and will decrease the effective focal length. The combination of these lenses will depend on their placement and individual focal lengths.

5. Are there any limitations to the effective focal length of multiple lenses?

Yes, there are limitations to the effective focal length of multiple lenses. The combined focal length cannot be less than the focal length of the lens with the shortest focal length. Additionally, lenses placed too close together may cause distortion or reduce the effectiveness of the overall focal length. It is important to carefully consider the placement and combination of lenses to achieve the desired effective focal length.

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