Geometric Optics - Light and Mirrors PDF

Geometric Optics  Main Topics The Reflection of Light Forming Images with a Plane Mirror Spherical Mirrors Ray Tracing and the Mirror Equation The Refraction of Light Ray Tracing for Lenses The Thin-Lens Equation Dispersion and the Rainbow ...

Geometric Optics  Main Topics The Reflection of Light Forming Images with a Plane Mirror Spherical Mirrors Ray Tracing and the Mirror Equation The Refraction of Light Ray Tracing for Lenses The Thin-Lens Equation Dispersion and the Rainbow  The Reflection of Light If a stone is dropped into a pond, circular waves emanate from the point where it landed. Rays, perpendicular to the wave fronts, give the direction in which the waves propagate.  The TheReflection ofLight Reflection of Light As one moves farther from a point wave source, the wave fronts become more nearly flat.  The TheReflection ofLight Reflection of Light The law of reflection states that the angle of incidence equals the angle of reflection:  The TheReflection ofLight Reflection of Light Reflection from a smooth surface is called specular reflection; if the surface is rough, it is diffuse reflection.  Forming Images with a Plane Mirror Light reflected from the flower and vase hits the mirror. Obeying the law of reflection, it enters the eye. The eye interprets the ray as having had a straight-line path, and sees the image behind the mirror.  Forming Images with a Plane Mirror Properties of Mirror Images Produced by Plane Mirrors: A mirror image is upright, but appears reversed right to left. A mirror image appears to be the same distance behind the mirror that the object is in front of the mirror. A mirror image is the same size as the object.  Forming Forming Images withaaPlane Images with PlaneMirror Mirror A corner reflector reflects light parallel to the incident ray, no matter the incident angle.  Spherical Mirrors A spherical mirror has the shape of a section of a sphere. If the outside is mirrored, it is convex; if the inside is mirrored, it is concave.  Spherical Mirrors Spherical Mirrors Spherical mirrors have a central axis (a radius of the sphere) and a center of curvature (the center of the sphere).  Spherical Spherical Mirrors Parallel rays hitting a spherical mirror come together at the focal point (or appear to have come from the focal point, if the mirror is convex).  Spherical Spherical Mirrors This is a ray diagram for finding the focal point of a concave mirror.  Spherical Mirrors Spherical Mirrors For a convex mirror, the focal length is negative, as the rays do not go through the focal point. The opposite is true for a concave mirror.  Spherical Spherical Mirrors We have made the assumption here that the rays do not hit the mirror very far from the principal axis. If they do, the image is blurred; this is called spherical aberration, and can be remedied by using a parabolic mirror instead.  Spherical Mirrors Spherical Mirrors When the Hubble Space Telescope was first launched, its optics were marred by spherical aberration. This was fixed with corrective optics.  Ray Tracing and the Mirror Equation We use three principal rays in finding the image produced by a concave mirror. The parallel ray (P ray) reflects through the focal point. The focal ray (F ray) reflects parallel to the axis. The center-of-curvature ray (C ray) reflects back along its incoming path.  Ray RayTracing the Mirror Tracing and the Mirror Equation Equation These three rays are illustrated here.  Ray RayTracing the Mirror Tracing and the Mirror Equation Equation This image shows how these three rays are used to find the image formed by a convex mirror. The image is located where the projections of the three rays cross. The size of the image can also be determined.  Ray RayTracing the Mirror Tracing and the Mirror Equation Equation The process is similar for a concave mirror, although there are different results depending on where the object is placed.  Ray RayTracing the Mirror Tracing and the Mirror Equation Equation We derive the mirror equation using the ray diagrams:  Ray RayTracing Tracing and and the Mirror Equation Equation Using the similar triangles and the fact that f = ½ R, we get the mirror equation: Here, do is the distance from the mirror to the object, di is the distance from the mirror to the image, and f is the focal length. Ray RayTracing the Mirror Tracing and the Mirror Equation Equation  Ray RayTracing the Mirror Tracing and the Mirror Equation Equation We can also find the magnification:  Ray RayTracing Tracing and and the Mirror Equation Equation Here are the sign conventions for concave and convex mirrors: