and Optical Instruments Image Formation and Optical Instruments

• Simple Lens A simple lens is an optical device which takes parallel light rays and focuses them to a point. This point is called the focus or focal point f • f Snell’s Law, applied at each point on the surface, determines where the light comes to a focus.

Simple Lens Convex lens compared to pair of prisms Concave lens compared to pair of prisms

Image Formation in a Lens The formation of images by a lens can be determined using two alternative approaches: Using ray tracing. In this case a small number of characteristic rays are used. b) Using the Thin Lens equation and the Magnification equation. These equations relate the object and image distances, to the focal distance and magnification, respectively.

Image Formation in a Lens – Ray Tracing The three basic light rays used in ray tracing: A ray which leaves the object parallel to the axis, is refracted to pass through the focal point (P). 2. A ray which passes through the lens’s center is undeflected (M). 3. A ray passing through the focal point (as shown) is refracted to end up parallel to the axis (F).

Images Formed by a Convex Lens Object between 2f and f Image is inverted, real enlarged. Object between f and lens Image is upright, virtual, and enlarged.

Images Formed by a Concave Lens Object beyond 2f. Image is upright, virtual, reduced. Object between f and lens.

The Thin Lens Equation

Sing Conventions 1. Converging or convex lens • focal length is positive • image distance is positive when on the other side of the lens (with respect to object) • height upright is positive, inverted is negative 2. Diverging or concave lens • focal length is negative • image distance is always negative (on the same side of the lens as the object) • height upright is positive, inverted is negative

The image is twice as large as the object and is located 15 cm from the lens. Find: The focal length The object distance

An object of height 3 cm, is placed 12 cm in front of a diverging lens with a focal length of – 7.9 cm. Use ray tracing to form the image Use the thin lens equations to find the image distance and size

An object of height 3 cm, is placed 12 cm in front of a diverging lens with a focal length of – 7.9 cm. Use ray tracing to form the image Use the thin lens equations to find the image distance and size

An object of height 3 cm, is placed 12 cm in front of a diverging lens with a focal length of – 7.9 cm. Use ray tracing to form the image Use the thin lens equations to find the image distance and size

The Lensmaker’s Formula The lens formula correlates the focal distance, the object distance, and the image distance [1/f =1/l + 1/l’] The lensmaker’s formula gives the focal distance f, as a function of R1 and R2, the radii of curvature of the two surfaces of the lens.

The Human Eye The eye produces a real, inverted image in the retina. The Ciliary muscles change the shape of the lens, adjusting the focal length according to the object distance. The amount of light that enters the eye is controlled by the iris, that expands or contracts to adjust the pupil size

The Camera The camera forms a real, and inverted image, on a photographic film, or a solid state sensor The camera focuses by moving the lens back and forth. The aperture of the camera can be adjusted: Small f-number  large aperture The amount of light that enters the camera is controlled by the f-number (i.e 5.6) and the shutter speed (i.e.1/250).

The Angular Size of an Object The image of the object subtends an angle  on the retina.   ho / do The larger , the larger the object appears to be. The closest object distance at which the eye can focus is the near point N. N  25 cm (young) N  40 cm (not so young)

The Magnifying Glass Object at near point:   ho / N If a lens with focal distance f (f < N), is placed in front of the eye, and the object is placed at f, the image forms at infinite, with angular size ’  ho / f. Since f < N  ’  , and the object appears magnified. Angular magnification: M = ’ /   N / f Tan   

The Compound Microscope The objective has short focal distance. The object is placed just beyond the focal point. A real, inverted, enlarged, image is formed, at or near the focus of the eyepiece. The eyepiece works as a magnifier, producing a further magnified image. The distance between the lenses is larger than the sum of focal lengths. The total magnification is the product of each lens magnification. M  - (di / fobjective) (N / feyepiece)

The Telescope Telescopes deal with objects that are infinitely far away. The image formed by the objective is at its focal point, (and at the focal point of the eyepiece). The eyepiece works as a magnifier, producing a further enlarged image. The distance between lenses is about the sum of the focal lengths. The angular magnification is M = ’ /  = fobjective / feyepiece