Module 1-4Basic Geometrical Optics

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 LensesFigure 3a Positive lens

Image Formation with LensesFigure 3b Negative lens

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 LensesFigure 4b two focal points, for

negative 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 LensesFigure 5 Defining quantities for

image formation with a thin lens

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