Final answer:
The total power of two glued lenses is the sum of their individual powers because power is inversely proportional to focal length. The power of a lens is defined as P = 1/f, and for two lenses, P_total = P1 + P2. The angular magnification formula is M = 1 + D/f, which applies when the eye is close to the lens.
Step-by-step explanation:
In optics, when two lenses with focal lengths f₁ and f₂ are glued together, the total power of the combination is simply the sum of their individual powers. The power P of a lens is defined as P = 1/f, where f is the focal length of the lens in meters. Thus, for the two lenses, the powers would be P₁ = 1/f₁ and P₂ = 1/f₂. The combined power Ptotal is then Ptotal = P₁ + P₂ = 1/f₁ + 1/f₂.
For example, if a diverging lens has a focal length of 20 cm, first we convert it to meters (0.20 m) to find the power in diopters. Substituting this into the power equation, we get P = 1/0.20 m = 5 diopters, indicating a negative power since it is a diverging lens.
The angular magnification (sometimes given as magnifying power) of a convex lens for an object very close to the lens can be represented as M = 1 + D/f, where D is the nearest clear vision distance for the human eye (usually taken as 25 cm or 0.25 m).