Pages used and edited with permission (CC BY-SA 2.5). The eye manages this by varying the power (and focal length) of the lens to accommodate for objects at various distances. Power of a Lens is one of the most interesting concepts in ray optics. It goes straight through. Principal Ray II is headed straight for the head of the object along a line that is parallel to the principal axis of the lens. Your email address will not be published. Extinction ratio (re) The ratio of a logic-one power level (P1) relative to a logic-zero power level (P0). LENSMAKER’S EQUATION The original formula for lens power can be written substituting (u-1)/r1 for D1 and (u-1)/r2 for D2 to arrive at Dn = (u-1)/r1 + (u-1)/r2, aka the Lensmaker’s Equation. By inspection, the two shaded triangles are similar to each other. Total attenuation is the sum of all losses. Then, for the second lens, the object distance and the image distance are measured relative to the plane of the second lens. Thus: Recall the conventions stated in the last chapter: In the case at hand, we have an inverted image, so \(h'\) is negative, so \(|h'|=-h'\). Here’s the diagram from the last chapter. Thus, we can write the magnification as: Here’s another copy of the same diagram with another triangle shaded. Your email address will not be published. I know that the Optical output power of LED (watts) = N( a linear factor) × Voltage drop across resistor (volts) Pout = N × Vres * Pout is the optical output power in watts (W). Two-Lens Systems To calculate the image of a two-lens system, one simply calculates the position of the image for the lens that light from the object hits first, and then uses that image as the object for the second lens. Also, I have labeled the sides of those two triangles with their lengths. This means that you can calculate the power of a lens using radii of curvature of two surfaces and the refractive index of the lens material. then \(o_2\), the object distance for the second lens, is \(4\) cm. You might well wonder what quantity the given number is a value for, and what the units should be. We have been using the principal rays to locate the image, as in the following diagram: in which I have intentionally used a small lens icon to remind you that, in using the principal ray diagram to locate the image, we don’t really care whether or not the principal rays actually hit the lens. Optical polarization is often a major consideration in the construction of many optical systems, so equations for working with polarization come in handy. Finally, when light comes out at z L, its power is much higher compared to what it was at z 0 . Consider for instance the case of a converging lens with an object more distant from the plane of the lens than the focal point is. The optical cavity thus obtained is called a Fabry-Perot cavity and is shown below. While we have derived it for the case of an object that is a distance greater than the focal length, from a converging lens, it works for all the combinations of lens and object distance for which the thin lens approximation is good. If one follows a guided mode through one complete roundtrip of the cavity, one finds that the change in optical power after one complete roundtrip is, R R e ag 2L ~ ~ 1 2 But \(\frac{h'}{h}\) is, by definition, the magnification. Because the lens-to-retina distance does not change, the image distance d i must be the same for objects at all distances. Together with our definition of the magnification \(M=\frac{h'}{h}\), the expression we derived for the magnification \(M=-\frac{i}{o}\), and our conventions: The lens equation tells us everything we need to know about the image of an object that is a known distance from the plane of a thin lens of known focal length. 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