module 1-4 basic geometrical optics. image formation with lenses lenses are at the heart of many...
TRANSCRIPT
Image Formation with LensesLenses are at the heart of many
optical devices, not the least of which are cameras, microscopes, binoculars, and telescopes.
Lenses are essentially light-controlling elements, used primarily for image formation with visible light, but also for ultraviolet and infrared light.
Image Formation with LensesFunction of a lensA lens is made up of a transparent
refracting medium, generally of some type of glass, with spherically shaped surfaces on the front and back.
A ray incident on the lens bends at the front surface, propagates through the lens, and bends again at the rear surface, according to Snell’s law.
See Figure 1, next slide
Image Formation with LensesFigure 1: Refraction of light rays by
a lenswhere:
n = index of refractiont = axial thickness
Image Formation with LensesTypes of lensesIf the axial thickness t of a lens (see
Figure 1) is small compared with the radii of curvature r1 and r2 of its surfaces, it can be treated as a thin lens.
If the thickness of a lens is not negligible compared with the radii of curvature of its faces, it must be treated as a thick lens.
NOTE: In this basic introduction of geometrical optics, however, we shall deal only with thin lenses.
Image Formation with LensesConverging and diverging thin
lensesIn Figure 2, are shown shapes of
several common “thin” lenses.Figure 2
Image Formation with LensesFocal points of thin lensesThe focal points of lenses are
defined in terms of the effect that lenses have on incident parallel light rays and plane wave fronts.
Figure 3 shows parallel light rays and their associated plane wave fronts incident on a positive lens (Figure 3a) and a negative lens (Figure 3b).
Image Formation with LensesFor the positive lens, refraction of
the light by the lens brings it to a focal point F (real image) to the right of the lens.
For the negative lens, refraction of the light by the lens causes it to diverge as if it were coming from focal point F located to the left of the lens.
Image Formation with LensesFor thin lenses, there are two
focal points, symmetrically located on each side of the lens, since light can approach from either side of the lens.
Figure 4a two focal points, for positive lenses
Image Formation with LensesLens formulas for thin lensesFor thin lenses convenient formulas can be
used to locate the image mathematically. Figure 5 shows the essential elements that
show up in the final equations, relating object distance p to image distance q, for a lens of focal length f with radii of curvature r1 and r2 and refractive index ng.
For generality, the lens is shown situated in medium of air with refractive index n = 1
Image Formation with Lenses
Equations for thin lens calculations
where p (do) is the object distance (from object to lens vertex V )q (di) is the image distance (from image to lens vertex V )f is the focal length (from either focal point F or F 'to the lens vertex V )
Image Formation with Lenses
Equations for magnification calculations
where m is the magnification produced by the lens (ratio of image size to object size)hi is the vertical transverse size of the image, measured perpendicularly to the optical axisho is the vertical transverse size of the object, measured perpendicularly to the optical axisp and q are object and image distance respectively