THIN LENSES

Thin lenses Convex Converging f > 0 f Concave Diverging f < 0

First and second focal points of a converging thin lens First and second focal points of a converging thin lens. The numerical value of f is positive.

Construction used to find the image position for a thin lens.

Three easy rays for ray-tracing Objects and images S S’ x y f f Three easy rays for ray-tracing Thin lens equation magnification

S’, f and S are all positive Reading the signs In this diagram The object is “upstream” of the lens. The lens is a converging lens. The image is a real image through which light rays actually pass, and it is “downstream” of the lens. S’, f and S are all positive

Formation of images by a thin converging lens for various object distances.

Two types of images Real image i > 0 , so light rays pass through image point (“in front” of mirror) Inverted Virtual image i < 0 , so light rays do not pass through image point (“behind” mirror) Upright

First and second focal points of a diverging thin lens First and second focal points of a diverging thin lens. The numerical value of f is negative.

A negative lens Upright, virtual image 37.5% as large as object S = +50 cm f = -30 cm S’ = -18.75 cm m = 0.375 Upright, virtual image 37.5% as large as object

Principal-ray diagram for an image formed by a thin diverging lens.

Optical Instruments

A typical single lens reflex camera A typical single lens reflex camera. The lens has many elements cemented together to form a single compound lens.

The larger image size with a larger value of f corresponds to a smaller angle of view.

In a camera lens, larger f-numbers mean smaller aperture diameters. f-number = f / D where D = diameter of aperture

Overhead projector. The inexpensive plastic Fresnel lens is like an ordinary thick lens with the internal material removed.

The eye. The muscle contracts to change the focal length of the lens to image close objects.

Refractive errors for a myopic (nearsighted) eye and a hyperopic (farsighted) eye viewing a very distant object. The dashed blue curve indicates the correct position of the retina.

(a) An uncorrected hyperopic (farsighted) eye (a) An uncorrected hyperopic (farsighted) eye. (b) A positive (converging) lens gives the extra convergence needed for a hyperopic eye to focus the image on the retina. The virtual image formed by the converging lens acts as an object at the near point.

Microscope Basics Originally conformed to the German DIN standard Standard required the following real image formed at a tube length of 160mm the parfocal distance set to 45 mm object to image distance set to 195 mm Currently we use the ISO standard Object to Image Distance = 195 mm Mechanical tube length = 160 mm Focal length of objective = 45 mm

The Conventional Microscope Mechanical tube length = 160 mm Object to Image Distance = 195 mm Focal length of objective = 45 mm

The image produced by first lens acts as a virtual object for the second lens.