Relation for combination of two thick lenses

In summary, simple lenses can experience optical aberrations, but these can often be corrected by using a combination of lenses with complementary aberrations. Compound lenses, which consist of multiple simple lenses arranged in a specific way, can also help compensate for aberrations. In contact, the focal length of two thin lenses is additive, while separated lenses have a combined focal length determined by their distance. For thick lenses, there are more complex methods for determining the combined focal length.
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Simple lenses are subject to the optical aberrations discussed above. In many cases these aberrations can be compensated for to a great extent by using a combination of simple lenses with complementary aberrations. A compound lens is a collection of simple lenses of different shapes and made of materials of different refractive indices, arranged one after the other with a common axis.

The simplest case is where lenses are placed in contact: if the lenses of focal lengths f1 and f2 are "thin", the combined focal length f of the lenses is given by

42b3acf0ad19d7b15b4972ee9414eee1.png


Since 1/f is the power of a lens, it can be seen that the powers of thin lenses in contact are additive.

If two thin lenses are separated in air by some distance d, the focal length for the combined system is given by

988c6074e1c5cc622dd1f9cb30f5bb80.png

So what if we have two thick lenses?
Thanks in advance ,
 
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1. What is the relation for the combination of two thick lenses?

The relation for the combination of two thick lenses is given by the lens maker's formula, which states that the combined power of two lenses is equal to the sum of their individual powers. This can be expressed as: Fcombined = F1 + F2 where Fcombined is the combined power, F1 is the power of the first lens, and F2 is the power of the second lens.

2. How do you calculate the combined power of two thick lenses?

The combined power of two thick lenses can be calculated using the lens maker's formula, which states that the combined power is equal to the sum of the individual powers. This formula can be written as: Fcombined = F1 + F2 where Fcombined is the combined power, F1 is the power of the first lens, and F2 is the power of the second lens.

3. What is the formula for calculating the combined focal length of two thick lenses?

The formula for calculating the combined focal length of two thick lenses is similar to the lens maker's formula, but it is given in terms of the focal lengths instead of the powers. The formula is: fcombined = (f1 * f2) / (f1 + f2 - d) where fcombined is the combined focal length, f1 and f2 are the focal lengths of the individual lenses, and d is the distance between the two lenses.

4. Can the combined power of two thick lenses be negative?

Yes, the combined power of two thick lenses can be negative if the individual powers of the lenses have opposite signs. This indicates that the two lenses are diverging and the combination of the two will result in a weaker overall power. For example, if one lens has a power of +5 diopters and the other has a power of -3 diopters, the combined power would be +2 diopters.

5. How does the distance between two thick lenses affect their combined power?

The distance between two thick lenses, also known as the lens separation, can affect their combined power. The lens maker's formula and the formula for combined focal length both include the lens separation term (d). As the distance between the lenses increases, the combined power decreases and vice versa. This is because a greater distance between the lenses allows for more diverging light rays to pass through, resulting in a weaker overall power.

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