Seeing an Object. 6: Geometric Optics (Chapters 34)

Transcription

1 Seeing an Object 6: Geometric Optics (Chapters 34) Phys130, A01 Dr. Robert MacDonald Light rays from each point on the go everywhere. Some light from each point reaches the. 2 virtual image As long as only one ray from each point on the reaches the, we see the clearly. 3 When we look in a mirror, the rays that reach the appear to come from an behind the mirror. What we see is called a virtual image. As far as the is concerned, it s the same as a real image (or an ). But the light that we see is not coming from the virtual image, unlike a real image. 4

2 Images & Plane Surfaces We can use the geometry of rays to figure out where images get formed. We ll look at reflection and refraction at a plane (flat) surface first. We ll start by working with point s and see where all the rays go. Since light is emitted from each point on an in all directions, we can say that extended s are composed of points. We ll establish some basic rules using point s, then see how they work with extended s. 5 Image in Reflection When the light from a point strikes a plane mirror, the reflected light appears to be all coming from behind the mirror (as you know). This point is called the image point, and is a useful way to describe the directions of the reflected rays. The location of the is called the point, and is a useful way to describe the directions of the rays before being reflected. The image is virtual. 6 (positive) image (negative) Fig Image Distance: Plane Mirror The two rays (OI and Oa) shown give where you d see the image depending on where you look. We can use the diagram to the right to show how the image s relates to the s. It turns out p = i for a plane mirror. Fig Sign Conventions Sign rule for the : When the is on the same side of the surface as the incoming light, the is positive. Otherwise it s negative. Sign rule for the image : When the image is on the same side of the surface as the outgoing light, the image is positive. Otherwise it s negative. (positive) image (negative) Fig

3 Extended Object For an extended, look at light from each point on the. For each point on the, we know the image i = p. Image is inside the mirror. Image =. Vertically the and image points are at the same level. So the whole image is the same size and orientation as the, and the same from the mirror surface. 9 Jargon: Fig If it s right side up, the image is erect. If the image is upside down we say it s inverted. For a plane mirror, the image is erect. Spherical Mirrors Spherical mirrors are useful they re used as magnifying mirrors (for shaving, makeup), surveillance mirrors, death rays, etc. First, some vocabulary (naturally). The centre of the mirror s sphere is called the centre of curvature. The midpoint of the mirror is called the vertex. The line through the centre of curvature and the vertex is called the optic axis. 10 optic axis centre of curvature radius of curvature vertex Sign: Radius of Curvature R R positive: outgoing light on the inside R negative outgoing light on the outside Curved mirror images Fig

4 Image of a Point Object Consider a point at point O on the optic axis. Light that goes up at some angle α will reflect and come back down at point I on the opposite side of the centre of curvature (but not the same away!) Light from the that goes through the centre of curvature (C) bounces off the vertex and comes back to point I. It turns out that, as long as α isn t too big, light at any angle α will cross point I, and I is the only location where this will happen. We get an image! 13 Fig The image is a real image. The light actually converges there. If you put a (small) screen there you d see a bright spot that looked just like the. If you look at the image point I directly, one of the rays passing through I will reach your, and you ll see the image directly. Note that many rays from point O all reach image point I. If we covered part of the mirror, there would still be light from the reaching the image point, so there would still be an image! Since the Law of Reflection works both ways, we could put an at point I and get an image at O. 14 Only works for small angles! Everything we re discussing about spherical mirrors is only true for rays that are close to the optic axis, so that the angles of reflection are small. These are called paraxial rays, meaning rays close to the axis. Block part of the mirror, and an image still forms; it s just dimmer. If the ray hits the mirror too far away from the axis, it won t cross the image point after reflection, and it ll mess up your image. This effect is called spherical abberation and is a problem with lenses as well. 16

5 Focal Point We ve seen that, for an on the centre of curvature, the image would be at the same point. (All the light bounces off the mirror and comes back.) We ve also see that, as the is moved away from the mirror, the image moves towards the mirror. What happens when the is infinitely far away? The only light rays that reach the mirror are all going pretty much the same direction; they re parallel. The image point for parallel incoming rays is called the focal point. The from that to the mirror is called the focal length. 17 Fig The focal length is the image when the is infinite. Off-axis Object Consider a point some off the optic axis. The different rays still arrive at a point they still form an image but the point is also off axis. Note that the point is off axis in the other direction. The from image point to axis won t necessarily be the same as from point to axis. We can use this to look at an extended. 18 Fig Aside: Principal Rays Light rays are coming out of the O in all directions. There are a set of rays that are particularly useful to look at, though, because the geometry is particularly simple for these rays. These are called the principal rays. 1: Incoming parallel to the optic axis. 2: Incoming ray passes through focal point, and is reflected parallel to the optic axis. 3: Incoming ray passes through the centre of curvature, bounces and comes back. 19 Fig : Incoming ray strikes the vertex (mirror middle) and reflects symmetrically around the optic axis.