When a light beam travels from a medium of a higher index of refraction to a medium of lower index of refraction, the refracted beam bends outwards, away from the normal. You can then imagine that at some point, you are going to hit where the refracted beam exits at 90 degrees. It is at this point where you hit the critical angle.
Reflection refraction and light 2010
INCLUDING TOTAL INTERNAL REFLECTION AND THE CRITICAL ANGLE Light: Reflection & Refraction
Law of Reflection <ul><li>The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection. </li></ul>
Diffuse Reflection <ul><li>Reflection off of rough surfaces such as clothing, paper, and the asphalt roadway leads to a type of reflection known as diffuse reflection . </li></ul>
Why does a dry road diffuse light, when a wet road specularly reflects.
Index of Refraction <ul><li>n = c/v </li></ul><ul><li>The larger the index, </li></ul><ul><li>the slower the </li></ul><ul><li>speed of light </li></ul>
Refraction Rules Light twists inward when entering medium of higher index of refraction
Refraction Rules Light twists outward when entering medium of lower index of refraction
Understanding Refraction Wheels on axle rolls along a smooth sidewalk and onto grass. Which picture path is followed? What happens if the motion is reversed?
Understanding Refraction One side of wave front slows down, and the entire train of fronts twists.
Illustrating Cart Analogy Right front wheel slows down before left front Left front wheel slows down before right front
Snell’s (Sahl’s) Law (a history) <ul><li>Ibn Sahl was an Arabian Mathematician and optics engineer associated with the court of Baghdad. In 984 he wrote a treatise On Burning Mirrors and Lenses in which he set out his understanding of how curved mirrors and lenses bend and focus light. Ibn Sahl is credited with discovering the law of refraction, usually called Snell's law. </li></ul><ul><li>In 1621, Willebrord Snellius (Snel) derived a mathematically equivalent form, that remained unpublished during his lifetime. </li></ul>
Snell’s Law <ul><li>Snell discovered that the ratio between the sine of the incident and refracted angles is equal to the ratio of the incident and refracted velocities. </li></ul>
Snell’s Law continued <ul><li>Because the velocity of light is extremely difficult to measure, it is more practical to use the indices of refraction. Due to the fact that the velocity is inversely proportional to the index of refraction, you get… </li></ul><ul><li> </li></ul><ul><li> Or… </li></ul>
Law of Refraction: Snell's Law Right front wheel slows down first. Snell's Law: n2 sin Q2 = n1 sin Q1
Snell's Law Example n 1 = 1.0 (air) n 2 = 1.52 (glass) Q 1 = 30 degrees ------------------------ n 2 sin Q 2 = n 1 sin Q 1 1.52 sin Q 2 = 1.0 sin 30 sin Q 2 = 0.33 Put calculator in Mode Degree Q 2 = sin -1 (0.33) = 19.3 degrees
Apparent Depth in Water Light exits into medium (air) of lower index of refraction, and turns left.
More Apparent Depth Spear-fishing is made more difficult by the bending of light. To spear the fish in the figure, one must aim at a spot in front of the fish
Refraction at Sunset Why does the sun appear to be flattened at sunset? --------------------------------------------------- The sun actually falls below below the horizon, i.e., it "sets", a few seconds before we see it set.
Displacement through a Slab of Glass Entering and exiting rays are displaced from each other, but parallel.
Internal Reflection All rays reflect internally, but the top three rays reflect only a small percentage internally; most energy leaves the prism. The fourth and fifth rays are reflected 100 % internally.
Critical angle… <ul><li>An incident angle at which the refracted angle is 90 o </li></ul><ul><li>Note: This can only happen in a case when light travels from a higher index of refraction to one with a lower index of refraction. </li></ul>
Critical Angle Calculation What must be Q 1 to get Q 2 = 90 deg ? Snell's Law: n 1 sin Q 1 = n 2 sin Q 2 = n 2 sin 90 sin Q 1 = n 2 / n 1 ------------------------------ Assume water to air: n 1 = 1.33 n 2 = 1.00 q 1 = sin -1 (0.752) = 48.8 degrees Q c = critical angle = 48.8 degrees
Cone of Light Crictical angle for water = 48.8 degrees Light within the 48.8 degree cone is detected by fish, while nothing in the air outside that cone can be seen. The only light reaching the fish outside the cone is that light (not shown) which is reflected off the bottom of the pool.
Critical Angle of Diamond n = 2.419 Q c = sin -1 (1.00/2.419) = 24.42 degrees 90.00 - 24.42 = 65.58 degrees Light outside of 65.58 degree cone is reflected back inside. Virtually all light entering the top face of the diamond is reflected internally.
Total internal reflection <ul><li>When incident light is at an angle greater than the critical angle, the light will reflect instead of refract. </li></ul><ul><li>When there is total internal reflection, the light will obey the law of reflection. </li></ul>