Lecture 18 Lens Examples In this lecture we ll look as a view common examples of optical instruments practical devices that create and manipulate images Before that though we need to consider some of the practical difficulties in using lenses and mirrors to form images of objects Effects that cause images to not focus perfectly are called aberrations One such aberration arises from the fact that not all rays are paraxial And rays that are farther from the center of a spherical surface focus at different points This effect is called spherical aberration and occurs for both spherical mirrors and spherical lenses For mirrors spherical aberration can be eliminated by using a parabolic rather than spherical shape For a parabola all rays parallel to the axis focus at the same point no matter how far from the axis they are The Mirror Lab on campus under the football stadium produces large high quality parabolic mirrors for use in telescopes Another aberration arises due to effects of dispersion We already know that the index of refraction depends upon the wavelength of light Therefore different wavelengths colors passing through a lens can t all focus at exactly the same spot This is known as chromatic aberration Can be reduced by combining lenses with different properties Examples of Optical Instruments A camera is one example of an optical instrument Light enters when the shutter is opened and images are focused behind the lens onto film or in the case of digital cameras onto a set of light sensitive detection elements The lens has a fixed focal length but we want to capture images of objects as various distances from the camera done by mechanically varying the distance from the lens to the film i e getting the right q for a given p Other practical considerations to reduce spherical aberrations want light to enter only near center of lens small aperture for the shutter but that means not much light gets in image will be dim unless shutter is held open for a long time The optical instrument most familiar to us is the eye Focuses images on the retina which the brain then interprets as objects As with the camera we want to be able to focus images of objects at different distances the eye achieves this by changing the shape and thus the focal length of the lens the lens is a soft material that can be pulled into a thinner shape by muscles surrounding it this is called accomodation and appears to us to be instant and automatic Vision Problems In some cases the focal length of the lens does not match the distance to the retina If rays from near objects tend to focus behind retina person is farsighted can be corrected with converging lens If rays from far objects then to focus in from of retina person is nearsighted can be corrected with diverging lens Ophthalmologists use the term diopters to describe a lens but that s just a code word the lens power in diopters is just one over the focal length in meters Magnifying Glass This is another very common optical device Aim is to produce an upright image that looks bigger than the object By looks bigger we mean that it subtends a larger angle Looks smaller Looks bigger In principle we can make any object look bigger just by bringing our eye closer to it but there s a limit accomodation stops working for objects that are too close the near point is the distance to the closest object we can focus on For an object of a given size h then the largest angle it can subtend is h tan o o pn Near point What happens if we place the object in front of a lens such that the image appears at pn Then the object must be at 1 1 1 p pn f pn f p pn f The angle subtended by the image is h h h h qh h M q h q q pq p So the factor by which the object looks bigger is h p pn m o h pn p pn pn f pn 1 pn f f f pn f Note that we get substantial magnification only when f is much less than pn The Microscope To achieve greater magnification than the simple magnifying glass we can use a microscope this device consists of two converging lenses 1 The objective lens has a short focal length fo 2 The eyepiece lens has fe of a few cm The two lenses are separated by a distance much bigger than fo or fe L fo Objective Eyepiece Note that the object is placed just outside fo so that the image appears almost at L Therefore the magnification by the objective is M q f o p L This image serves as the object for the eyepiece lens which acts as a magnifying glass i e this lens increases the apparent size by pn m fe Thus the total magnifying power is L pn Mm fo fe This can be a factor of several hundred