Light: Reflection and Refraction, Summaries of Law

Download Light: Reflection and Refraction and more Summaries Law in PDF only on Docsity! Phys102 Lecture 23/24 Light: Reflection and Refraction Key Points • The Ray Model of Light • Reflection and Mirrors • Refraction, Snell’s Law • Total internal Reflection References SFU Ed: 32-1,2,3,4,5,6,7. 6th Ed: 23-1,2,3,4,5,6. Light very often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization, but is very useful for geometric optics. The Ray Model of Light What you see when you look into a plane (flat) mirror is an image, which appears to be behind the mirror. Image Formation by a Plane Mirror This is called a virtual image, as the light does not go through it. The distance of the image from the mirror is equal to the distance of the object from the mirror. Image Formation by a Plane Mirror 32-2 Reflection; Image Formation by a Plane Mirror Example 32-2: How tall must a full-length mirror be? A woman 1.60 m tall stands in front of a vertical plane mirror. What is the minimum height of the mirror, and how close must its lower edge be to the floor, if she is to be able to see her whole body? Assume her eyes are 10 cm below the top of her head. Parallel rays striking a spherical mirror do not all converge at exactly the same place if the curvature of the mirror is large; this is called spherical aberration. Formation of Images by Spherical Mirrors If the curvature is small (small θ), the focus is much more precise; the focal point is where the rays converge. Formation of Images by Spherical Mirrors Using geometry, we find that the focal length is half the radius of curvature: Spherical aberration can be avoided by using a parabolic reflector; these are more difficult and expensive to make, and so are used only when necessary, such as in research telescopes. Formation of Images by Spherical Mirrors The intersection of these three rays gives the position of the image of that point on the object. To get a full image, we can do the same with other points (two points suffice for many purposes). Formation of Images by Spherical Mirrors Geometrically, we can derive an equation that relates the object distance, image distance, and focal length of the mirror: Formation of Images by Spherical Mirrors We can also find the magnification (ratio of image height to object height): The negative sign indicates that the image is inverted. This object is between the center of curvature and the focal point, and its image is larger, inverted, and real. Formation of Images by Spherical Mirrors If an object is outside the center of curvature of a concave mirror, its image will be inverted, smaller, and real. Formation of Images by Spherical Mirrors Formation of Images by Spherical Mirrors Example 32-6: Object closer to concave mirror. A 1.00-cm-high object is placed 10.0 cm from a concave mirror whose radius of curvature is 30.0 cm. (a) Draw a ray diagram to locate (approximately) the position of the image. (b) Determine the position of the image and the magnification analytically. For a convex mirror, the image is always virtual, upright, and smaller. Formation of Images by Spherical Mirrors In general, light slows somewhat when traveling through a medium. The index of refraction of the medium is the ratio of the speed of light in vacuum to the speed of light in the medium: Index of Refraction Light changes direction when crossing a boundary from one medium to another. This is called refraction, and the angle the outgoing ray makes with the normal is called the angle of refraction. Refraction: Snell’s Law Example 32-9: Apparent depth of a pool. A swimmer has dropped her goggles to the bottom of a pool at the shallow end, marked as 1.0 m deep. But the goggles don’t look that deep. Why? How deep do the goggles appear to be when you look straight down into the water? Visible Spectrum and Dispersion This spreading of light into the full spectrum is called dispersion. If light passes into a medium with a smaller index of refraction, the angle of refraction is larger. There is an angle of incidence for which the angle of refraction will be 90°; this is called the critical angle: Total Internal Reflection If the angle of incidence is larger than this, no transmission occurs. This is called total internal reflection. Total Internal Reflection; Fiber Optics Optical fibers also depend on total internal reflection; they are therefore able to transmit light signals with very small losses.