Final answer:
The combined focal length 'f' of two thin lenses with focal lengths 'f₁' and 'f₂' in contact is determined by their lens powers, which add together according to 1/f = 1/f₁ + 1/f₂.
Step-by-step explanation:
When two thin lenses with focal lengths f₁ and f₂ are kept in contact with each other, we can describe their combined effect in terms of lens power. The power of a lens, represented as p, is the inverse of the focal length (p = 1/f). For two lenses in contact, the total power P is simply the sum of their individual powers: P = p₁ + p₂, where p₁ = 1/f₁ and p₂ = 1/f₂.
The focal length of the combination can be found by taking the inverse of the total power, so 1/f = P = 1/f₁ + 1/f₂. This gives us the combined focal length f of the two lenses when they are in contact. The thin-lens equation assumes that lenses are thin enough that the distance light travels within the lens material is negligible, which is why this simple additive relationship holds true.
Therefore, by using the concept of lens power and the nature of thin lenses, we can prove that the combined focal length of two lenses in contact is given by the equation 1/f = 1/f₁ + 1/f₂.