Reflection Most objects we see reflect light rather than emit their own light.
A B Principle of Least Time • Fermat's principle - light travels in straight lines and will take the path of least time to strike mirror and reflect from point A to B Wrong Path True Path MIRROR
Law of Reflection “The angle of incidence equals the angle of reflection.” This is true for both flat mirrors and curved mirrors.
Normal Line Angle of Reflection Angle of Incidence A B = MIRROR
Tangent Incidence Normal Reflection C F
Types of Reflection Specular Reflection - images seen on smooth surfaces (e.g. plane mirrors) Diffuse Reflection - diffuse light coming from a rough surface (cannot see a reflection of yourself)
Locating the Image for Plane Mirrors • Draw the image the same distance behind the mirror as the object is in front. • Draw a connector line from each object to each image. • If the connector line passes through the mirror, the image will be seen.
Mirror Images D A B E C C E A B D These lines are pointed to the only images that will be seen from each of the original locations (A-E) NOTE: No images will be seen from E
C F Light from Infinite Distance Focuses at the focal point
Two Rules for Locating the Image for Concave Mirrors • Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection
Two Rules for Concave Mirrors • Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection • Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection
C F Virtual Image
Mirror Equation: do> C f = 2 cm, C = 4 cm, ho = 2 cm, do = 5cm, di = ? 1/f = 1/do + 1/di 1/2 = 1/5 + 1/di 1/di = 1/2 - 1/5 = 0.5 – 0.2 = 0.3 di = 3.33 cm M = hi/ho = -di/do (-ho x di )/ do = hi hi = (-2 x 3.3)/5 hi = -1.3 cm M = - di / do = -0.66
Mirror Equation: C >do>f f = 2 cm, C = 4 cm, ho = 2 cm, do = 3 cm, di = ? 1/f = 1/do + 1/di 1/2 = 1/3 + 1/di 1/di = 1/2 - 1/3 = 0.5 – 0.333 = 0.167 di = 6.0 cm M = hi/ho = -di/do (-ho x di )/ do = hi hi = (-2 x 6)/3 hi = -4.0 M = - di / do = -2.0
Mirror Equation: do = f f = 2 cm, C = 4 cm, ho = 2 cm, do = 2 cm, di = ? 1/f = 1/do + 1/di 1/2 = 1/2 + 1/di 1/di = 1/2 - 1/2 = 0.5 – 0.5 = 0 di = no image
C F Virtual Image
Mirror Equation: do < f f = 2 cm, C = 4 cm, ho = 2 cm, do = 1 cm, di = ? 1/f = 1/do + 1/di 1/2 = 1/1 + 1/di 1/di = 1/2 - 1/1 = 0.5 – 1.0 = -0.5 di = -2.0 cm M = hi/ho = -di/do (-ho x di )/ do = hi hi = (-2 x -2)/1 hi = +4.0 M = - di / do = 2.0
C F Virtual Image
Real vs. Virtual Image • When a real image is formed, it still appears to an observer as though light is diverging from the real image location • only in the case of a real image, light is actually passing through the image location • Light does not actually pass through the virtual image location • it only appears to an observer as though the light was emanating from the virtual image location
Real Image C C F F Virtual Image
C F Will an image ever focus at a single point with a convex mirror? Therefore, the images you see are virtual!
Refraction Refraction is the bending of light when it passes from one transparent medium to another This bending is caused by differences in the speed of light in the media
Normal Line Less Dense More Dense
Normal Line #1 Fast Slow Light Beam AIR WATER AIR
Normal Line More Dense Less Dense
Normal Line #1 Fast Slow Fast Normal Line #2 Light Beam AIR WATER AIR
Refraction Examples • Light slows down when it goes from air into water and bends toward the normal. • An Analogy: A car slows down when it goes from pavement onto gravel and turns toward the normal. • An Illusion : Fish in the water appear closer and nearer the surface.
Refraction Observer AIR WATER False Fish True Fish
Atmospheric Refraction Our atmosphere can bend light and create distorted images called mirages.
Index of Refraction Equations • n = c/v = speed of light in a vacuum speed of light in medium
Index of Refraction Problem What is the speed of light in water, which has an index of refraction of 1.33? n = c/v v = c/n v = (2.998 x 108 m/s) / 1.33 V = 2.25 x 108 m/s