Geometric Optics The study of light divides itself into three fields geometric optics wave optics quantum optics Physics for Scientists Engineers 2 In the previous chapter we learned that light is an electromagnetic wave In the next chapter we will deal with the wave properties of light Spring Semester 2005 In this chapter we will deal with geometric optics in which we will treat light that travels in straight lines called light rays Lecture 36 Quantum optics makes use of the fact that light is quantized March 26 2005 Physics for Scientists Engineers 2 1 March 26 2005 Spherical Waves Physics for Scientists Engineers 2 2 Plane Waves Electromagnetic waves spread spherically from a source We can treat light waves from far away sources as plane waves whose wave front is traveling in a straight line The concentric yellow spheres shown below represent the spreading spherical wave fronts of the light emitted from the light bulb We can further abstract these traveling planes by vectors or arrows perpendicular to the surface of these planes The black arrows are the light rays which are perpendicular to the wave fronts at every point in space These planes can then be represented by a series of parallel rays or just one ray In this chapter we will treat light as a ray traveling in a straight line We can solve many problems geometrically and by various constructions Thus for the remainder of this chapter we will ignore our knowledge of the structure of light and attack a broad range of practical problems March 26 2005 Physics for Scientists Engineers 2 3 March 26 2005 Physics for Scientists Engineers 2 4 Reflection and Plane Mirrors Reflection and Plane Mirrors 2 Parallel rays incident on a plane mirror will be reflected such that the reflected rays are also parallel because every normal to the surface is also parallel A mirror is a surface that reflects light A plane mirror is a flat mirror For reflection from plane mirrors we have a simple rule for light rays incident on the surface of the mirror The law of reflection is given by This rule states that the angle of incidence i is equal to the angle of reflection r r i Images can be formed by light reflected from plane mirrors These angles are always measured from the normal which is defined to be a line perpendicular to the surface of the plane For example when you stands in front of a mirror you see your image in the mirror Reflected ray Normal to surface of mirror This image appears to be behind the mirror This type of image is referred to as a virtual image because it cannot be projected on a screen Plane mirror Incident ray March 26 2005 Physics for Scientists Engineers 2 5 March 26 2005 Mirror Image Physics for Scientists Engineers 2 6 Mirror Image 2 Images formed by plane mirrors appear to be reversed because the light rays incident on the surface of the mirror are reflected back on the other side of the normal di do A mirror image looks correct vertically Now let s discuss the left right question for the mirror image Again we construct the virtual image with two rays all rays behave the same way The image seen by the person can be constructed with two light rays as shown of course light rays are coming from every visible point of the person The image is upright meaning not upside down virtual implying that the image is formed behind the surface of the mirror The distance the person is standing from the mirror is called the object distance do and the distance the image appears to be behind the mirror is called the image distance di and for a plane mirror do di March 26 2005 Physics for Scientists Engineers 2 7 One can see that the real live person has his watch on his left hand and he sees that his virtual self has his watch on his right hand Thus when one looks in a mirror one sees an image that is upright but flipped left and right forming a mirror image March 26 2005 Physics for Scientists Engineers 2 8 Example Full length Mirror Example Full length Mirror Question The distance from the floor to the bottom of the mirror is 184 cm 8cm 2 88 cm A 184 cm 6 ft 1 2 inch tall person wants to buy a mirror so that he can see himself full length His eyes are 8 cm from the top of his head the angle of incidence equals the angle of reflection so the point on the mirror where the person can see the bottom of his feet will be half way between his eyes and the bottom of his feet What is the minimum height of the mirror Let us abstract the person as a 184 cm tall pole with eyes 8 cm from the top of the pole Similarly the difference between the top of the mirror and 184 cm is 8 cm 2 4 cm So the minimum length of the mirror is 184 cm 88 cm 4 cm 92 cm The required length of the Full length mirror is just half the height of the person wanting to see himself full length March 26 2005 Physics for Scientists Engineers 2 9 March 26 2005 Curved Mirrors However unlike the plane mirror the surface of a curved mirror is not flat Thus light rays that are parallel before they strike the mirror are reflected in different directions depending on the part of the mirror that they strike Depending of the shape of the mirror the light rays can be focused or made to diverge Suppose we have a spherical mirror where the reflecting surface is on the inside of the sphere We can abstract this sphere to a two dimensional semicircle The optical axis of the mirror is a line through the center of the sphere represented in this drawing by a horizontal dashed line Imagine that a horizontal light ray above the optical axis is incident on the surface of the mirror At the point the light ray strikes the mirror the law of reflection applies i r The normal to the surface is a radius line that points to the center of the sphere marked as C Thus we have a concave reflecting surface and the reflected rays will converge Physics for Scientists Engineers 2 10 Concave Spherical Mirrors When light is reflected from the surface of a curved mirror the light rays follow the law of reflection at each point on the surface March 26 2005 Physics for Scientists Engineers 2 11 March 26 2005 Physics for Scientists Engineers 2 12 Concave Spherical Mirror 2 Images with Concave Mirror Now let us talk about forming actual images with a concave mirror Now let us suppose that we have many horizontal light rays incident on this spherical mirror as shown For this explanation we choose the case where an object with height ho is placed a distance do from the mirror where do f Each light ray obeys the law …
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