Chapter 34 Geometric Optics Lecture by Dr. Hebin Li
Goals of Chapter 34 To see how plane and curved mirrors form images To learn how lenses form images To understand how a simple image system works
Reflection at a plane surface Light rays from a point radiate in all directions Light rays from an object point reflect from a plane mirror as though they came from the image point
Refraction at a plane surface Light rays from an object at P refract as though they came from the image point P.
Image formation by a plane mirror Object distance and image distance Sign rule for s: when the object is on the same side of the reflecting or refracting surface as the incoming light, s is positive; otherwise, it is negative Sign rule for s : when the image is on the same side of the reflecting or refracting surface as the outgoing light, s is positive; otherwise, it is negative
Characteristics of the image from a plane mirror The image is just as far behind the mirror as the object is in front of the mirror. s = s The lateral magnification is m = y /y. The image is virtual (no real light rays reach the image), erect, reversed, and the same size as the object 1 s + 1 s = 0
A flat mirror is simple, but A flat mirror is the simplest imaging optics. Yeah! So simple but wait a minute I love physics! https://www.youtube.com/watch?v=vbpxhfblvlu
The image is reversed The image formed by a plane mirror is reversed back to front.
Image formed by two mirrors The image formed by one surface can be the object for another surface. This property can lead to multiple images. Question: What if the angle is not 90 o?
Example: An extended object is placed in front of a flat mirror and an image of the object is formed by the mirror. Which of the following statements is incorrect? (A)The image is erect. (B) The image is a virtual image. (C) The image is reversed left and right. (D)The image has the same size as the object.
Spherical mirror with a point object Sign for R: when the center of curvature C is on the same side as the outgoing light, the radius of curvature is positive; otherwise, it is negative.
Focal point and focal length The focal length is half of the mirror s radius of curvature: f = R/2. (Lateral magnification)
Image of an extended object Figure below shows how to determine the position, orientation and height of the image.
Example: A spherical, concave mirror has a radius of curvature of 30 cm. An object of is 90 cm to the left of the vertex of the mirror. The length of the object is 5 cm. Use the graphical method (i.e. use principal rays) to find the location and length of the image. Compare your results by computing the location and length of the image using the object and image relationship equation.
Focal point and focal length of a convex mirror For a convex mirror, R is negative.
Image formation by a convex mirror The same equations describe the objectimage relationship. f = R/2
Graphical methods for mirrors Four principal rays for concave and convex mirrors. Four principal rays cross at the object and image.
Concave mirror with various object distances
Example: Rear-view Mirror: A mirror on the passenger side of your car is convex and has a radius of curvature with magnitude 18.0 cm. (a)another car is behind your car, 9.00 m from the mirror, and this car is viewed in the mirror by your passenger. If this car is 1.5 m tall, what is the height of the image? (b)what is the image distance? The mirror has a warning attached that objects viewed in it are closer than they appear. Why is this so?
Image of a point object at a spherical surface
Image of a point object at a spherical surface
Example: A Spherical Fish Bowl: A small tropical fish is at the center of a water-filled, spherical fish bowl 28.0 cm in diameter. (a)find the apparent position and magnification of the fish to an observer outside the bowl. The effect of the thin walls of the bowl may be ignored. (b)a friend advised the owner of the bowl to keep it out of direct sunlight to avoid blinding the fish, which might swim into the focal point of the parallel rays from the sun. Is the focal point actually within the pool?
Thin converging lens When a beam of rays parallel to the axis passes through a lens and converge to a point, such as a lens is called a converging lens (or positive lens). The points F 1 and F 2 are called focal points. The distance from a focal point to the center of lens is called focal length. The focal length is positive for a converging (positive) lens. Any lens that is thicker at its center than at its edges is a converging lens with positive f.
Image formed by a thin converging lens A thin converging lens can form an image of an extended object. The object-image relationship is described as 1 s + 1 s = 1 f The lateral magnification can be calculated as m = s s
Types of lenses Shown below are various types of lenses, both converging and diverging. Any lens that is thicker at its center than at its edges is a converging lens with positive f ; and any lens that is thicker at its edges than at its center is a diverging lens with negative f.
Thin diverging lens A beam of parallel rays incident on a diverging lens diverges. The focal length of a diverging lens is a negative quantity, so a diverging lens is also called a negative lens. Any lens that is thicker at its edges than at its center is a diverging lens with negative f. The object-image relationship is described by the same equation: 1 s + 1 s = 1 f The lateral magnification can be calculated as m = s s
Graphical methods for lenses We can determine the position and size of an image formed by a thin lens by using three principal rays. A ray parallel to the axis A ray through the center of the lens A ray through (or proceeding toward) the first focal point
Example: image formation by a converging lens Find the image position and magnification for an object at each of the following distances from a converging lens with a focal length of 20 cm: (a)50 cm; (b)40 cm; (c)15 cm.
Example: image formation by a diverging lens A thin diverging lens has a focal length of 20 cm. You want to use this lens to form an erect, virtual image that is 1/3 the height of the object. (a) Where should the object be placed? (b) Where will the image be?
The effect of object distance The object distance can have a large effect on the image. 1 s + 1 s = 1 f s = fs s f
Example: A lens forms an image of an object. The object is 16.0 cm from the lens. The image is 12.0 cm from the lens on the same side as the object. (a)what is the focal length of the lens? Is it converging or diverging? (b)if the object is 8.50 mm tall, how tall is the image? Is it erect or inverted? (c)draw a principal-ray diagram.
An image of an image The image formed by the first lens can act as an object for the second lens.
Example: A 1.20-cm-tall object is 50.0 cm to the left of a converging lens of local length 40.0 cm. A second converging lens, this one having a focal length of 60.0 cm, is located 300.0 cm to the right of the first lens along the same optic axis. (a)find the location and height of the image (call it I 1 ) form by the lens with a focal length of 40.0 cm. (b)i 1 is now the object for the second lens. Find the location and height of the image formed by the second lens.
Cameras When a camera is in proper focus, the position of the electronic sensor coincides with the position of the real image formed by the lens. 2016 Pearson Education Inc.
Camera lens basics The focal length f of a camera lens is the distance from the lens to the image when the object is infinitely far away. The effective area of the lens is controlled by means of an adjustable lens aperture, or diaphragm, a nearly circular hole with diameter D. Photographers commonly express the lightgathering capability of a lens in terms of the ratio f/d, called the f-number of the lens: 2016 Pearson Education Inc.
The eye The optical behavior of the eye is similar to that of a camera. 2016 Pearson Education Inc.
Defects of vision A normal eye forms an image on the retina of an object at infinity when the eye is relaxed. In the myopic (nearsighted) eye, the eyeball is too long from front to back in comparison with the radius of curvature of the cornea, and rays from an object at infinity are focused in front of the retina. 2016 Pearson Education Inc.
Nearsighted correction The far point of a certain myopic eye is 50 cm in front of the eye. When a diverging lens of focal length f = 48 cm is worn 2 cm in front of the eye, it creates a virtual image at 50 cm that permits the wearer to see clearly. 2016 Pearson Education Inc.
Farsighted correction A converging lens can be used to create an image far enough away from the hyperopic eye at a point where the wearer can see it clearly. 2016 Pearson Education Inc.
Angular size The maximum angular size of an object viewed at a comfortable distance is the angle it subtends at a distance of 25 cm. 2016 Pearson Education Inc.
The magnifier The angular magnification of a simple magnifier is: 2016 Pearson Education Inc.
The compound microscope 2016 Pearson Education Inc.
The astronomical telescope The figure below shows the optical system of an astronomical refracting telescope. 2016 Pearson Education Inc.
The reflecting telescope The Gemini North telescope uses an objective mirror 8 meters in diameter. 2016 Pearson Education Inc.