The focal length is the decisive number for the WeĬall the picture "real" if it is on the other side of the lens as seen from the object. That's what the geometric construction looks like. The Object O is at aĭistance of O cm, the image I will occur at a distance I cm. The lens has a focal length f always a positive number. Note: If what follows doesn't bore you to tears, you have a problem! "easy" fixes except using small apertures, i.e. Unlike optical lenses, however, there are usually no Problems as optical lenses, causing all kinds of trouble. It is of considerable interest for Materials Science that the electromagnetic lenses used in electron microscopes have pretty much the same "aberration" Sophisticated optical apparatus like your binocular or camera objective is not only extremely good but also dirt It is almost a miracle that we can see so well using a rather imperfect lens, and that Hemispherical lenses if the light rays coming in are inclined relative to the optical axis.Īnd so on. A similar effect applies even to perfectly Instead of a focal point you get a smeared out longish spot. The radius of curvature defining the surface of a lens is not exactly the same everywhere (probably true for the lens N = n( l) or dispersion curves that compensate the effects of chromatic "solution" is the achromatic lens, always a combination of two lenses made from different glasses with Refraction is a function of the wave length n = n( l). On the same focal point because we always have some dispersion and the index of Different wavelengths or "colors" are not focussed The solution might beĪspherical lenses but usually combinations of spherical lenses are used.Ĭhromatic aberration. Of course, lenses with small NA will not suffer much from sphericalĪberration but will also not transmit much light and thus produce "dark" pictures. The size of the lens see the picture below. The lens then has a small numerical aperture NA.Ī single lens is roughly the quotient of (possibly aperture defined) diameter / focal length i.e. The effect is small if some aperture keeps the light rays close to the opticĪxis. Spherical lenses, it becomes clear that light rays running not close to the center of the lens are focussed to a pointĭifferent from those close to the lens. Following Snellius' law, and tracing the light rays for ![]() Let's look very briefly on the first point. Point 1 to point 5 we move, of course, from geometric optics to wave All of the above may depend to some extent on the polarization of the light.Focal "points" have finite dimensions in in the.Intensity of the light is always attenuated or damped whenever it passes Some light is always reflected at interfaces between media with different indices of refraction.Real lenses have all kinds of problems called lens errors.With ideal lenses, we realize that some modifications need to be made: ![]() If we go one step beyond simple geometric optics Could there be an imaginary or even negative index of refraction? The answer is yes - as you will see later. ![]() N = e r 1/2 becomes troublesome if e < 0, which, as we know, is perfectly possible. Change the arrow directions in the picture above (or in all other pictures likeĪ not-so-nice thing might be that the definition of Obviously, all we need to know for this is the frequency dependence of theĭielectric constant e( n), something we have treated extensively before.Ī nice thing in geometric optics is that the direction of the light paths is always reversible. n = n( n) so we can construct light paths for the various frequencies (= colors) of visible light. Going a bit beyond that, we would also like Through optical devices like lenses or prisms. ![]() It already possible to construct light paths or light rays running Knowing only the index of refraction n makes Propagation c inside materials, frequency n and wavelength l in materials or in vacuum, is Know about Snellius law and some other basic optics parameters like the speed of The decisive material quantity in geometric optics (and beyond) is the index of refraction together with Snellius law. A light beam going through an optical grid is diffracted. " bending" of light beams around corners and all the other effects bringing aboutĭirectional changes and interference effects. " bending" or "flexing" of light beams at the interface between two different Reflection is, well, reflection always with (or dispersing or diverging) lenses allow to manipulate the light path, e.g. Convex (or collecting or converging) lenses and concave Have an index of refraction n > 1, and light hitting a transparent Optically transparent materials ("glass") The essence of basic high-school geometric optics is shown in the following pictures: 5.1.2 Basic Geometric Optics 5.1.2 Basic Geometric Optics
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