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The two lenses thus function together as a single lens, with a combined focal length. Note that this equation is only valid if the lenses are held very close together; otherwise the more general equation above should be used. We define the power of a lens as the reciprocal of its focal length: P = 1 / f . The units
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Each mirror has a radius of curvature r (which is infinite for the plane mirror) and a focal length f = 1 2r. By convention, distances are measured, along the central axis, as positive from the mirror in the direction of the object and negative away from the object.
The mirror equation enables one to calculate the image position from the object position and the radius of curvature of the mirror. A spherical mirror can also be characterized by its focal length. The focal length is the image distance when the object distance is infinity. From the mirror equation, we see that as p→∞ ⇒ 1 q = 1 f = 2 R
Two convex lenses of equal focal length are positioned in variable distances d and their principal focal length is calculated using the Newton's method. Initially, the equivalent optical power of the two-lens system is derived. This optical power is then plotted as a function of the distance d.
Apparent depth 1 MIRRORS AND LENSES f = ½ R Focal Length 1 + 1 = 1 a sinθ Thin Mirror and Lens Equation m= ℎ𝑖 ℎ =− CONSTANTS Magnification 𝐿 𝑃 = 1 Lens Power f number= 𝐷 F number Diverging Mirror/Lens R p q f Always virtual Converging Mirror/Lens 8.85×10 p > f real p < f virtual q real, inverted image
Focal Length and Object-Image Distances: The focal length, ƒ, of a lens is related to the radius of curvature, R, and inversely proportional to the index of refraction of the material. For our thin lenses, ƒ = 2R. Doubly convex or doubly concave thin lenses will have a focal
