REFRACTION Angle of refraction Dispersion Partial reflection & refraction Index of refraction Snell’s Law REFRACTION Refraction is the change in the direction of light when it crosses a boundary between two substances/media. A medium is the substance or material through which light is travelling. The plural of medium is media. Refraction • Occurs when the speed of light changes in different media • The particles in a medium slow down the passage of light waves • Different media slow down light by different amounts Refraction • Light only refracts at the boundary when it is entering or leaving a medium • The more that light slows down, the more the light is refracted Refraction in Water • Light rays change direction at the surface of the water • The image of the chest appears to be more shallow than the actual chest REFRACTION • refracted ray: the ray after crossing a boundary between media • angle of refraction: the angle between the refracted ray and the normal REFRACTION I nc id e nt r ay Angle of incidence r ef R d te ac y ra Normal Angle of refraction How Light Refracts • The part of the light beam that hits the medium first will slow down first Cause of Refraction Car Analogy • Car travelling at an angle towards a muddy surface • One front wheel hits muddy surface and slows down • Other wheels continue to move at a higher speed • Causes the path to bend REFRACTION Normal Angle of Refraction The angle of refraction is measured relative to the normal When moving from low to high refractive index light bends towards the normal (e.g. air glass) Angle of Refraction The angle of refraction is measured relative to the normal When moving from high to low refractive index light bends away from the normal (e.g. glass air) • The amount of refraction is different for each colour • A single beam of white light can be split into a rainbow of colours • Dispersion is the refraction of white light into separate wavelengths (colours) Dispersion Rainbows Partial Reflection & Refraction Refraction is often accompanied by reflection. Some of the light hitting the surface of a body of water reflects, and some refracts. Example: Pond water • Reflection: sky • Refraction: fish through the water Partial Reflection & Refraction • Ray diagrams can show both reflected and refracted light rays • Angle of reflection (r) follows the Law of Reflection (i = r) • Angle of refraction (R) can be calculated by Snell’s Law (see later slides) • Emergent ray: any ray of light that is leaving a medium (e.g. both reflected and refracted rays) Partial Reflection & Refraction • A large incident angle of light entering water results in nearly all the light reflecting. • As the angle of incidence gets smaller, more of the light refracts and less reflects. most reflecting (large angle of incidence) most refracting (small angle of incidence) most reflecting (large angle of incidence) Partial Reflection & Refraction • Silvered two way mirrors: plastic or glass with a special coating that reflects most light, but still allows some to be refracted • Results in a mirrored surface that you can see through, but others cannot. Partial Reflection & Refraction • • • “Don’t Miss A Sec” an architectural artwork by Monica Bonvicini, Dec 2003 Installed at a construction site across from London’s Tate Britain museum A public toilet enclosed within reflective glass walls that allow the user to see out but prevent those outside from seeing in http://www.snopes.com/photos/arts/toilet.asp Recall: Speed of Light 3.00 x 108 m/s 300 million m/s 300,000 km/s 1.08 x 1011 km/h 108 billion km/h However, it is impossible for light to move at this speed when particles get in the way Speed of Light Speed of light changes depending on the medium • Speed of light in a vacuum = 3.00x108 m/s • Speed of light in water = 2.26x108 m/s • Speed of light in acrylic = 1.76x108 m/s Index of Refraction • the amount by which a transparent medium decreases the speed of light • A ratio of the speed of light in a vacuum compared to the speed of light in a medium c = speed of light in a vacuum = a constant of 3.00x108 m/s v = speed of light in the medium = varies (e.g. water is 2.26x108m/s) (since units cancel, a refractive index does not have any units) Index of Refraction for various media Media Vacuum Index of Refraction 1.00 Air 1.0003 Carbon dioxide gas 1.0005 Ice 1.31 Pure water 1.33 Ethyl alcohol 1.36 Quartz 1.46 Vegetable oil 1.47 Olive oil 1.48 Acrylic 1.49 Table salt 1.51 Glass 1.52 Sapphire 1.77 Zircon 1.92 Cubic zirconia 2.16 Diamond 2.42 Gallium phosphide 3.50 Solve using GRASP Recall GRASP • Given: List the information given to you using symbols and numbers. Include units. • Required: List the item that needs to be solved. Use symbols. • Analysis: Write mathematical equation(s) that will be used. • Solution: Replace the equation with values listed in the Given. Solve the equation. • Phrase: Write the answer to the question in the form of a sentence. Given: v = 1.91 x 108 m/s c = 3.00 x 108 m/s Recall GRASP • Given: List the information given to you using symbols and numbers. Include units. • Required: List the item that needs to be solved. Use symbols. • Analysis: Write mathematical equation(s) that will be used. • Solution: Replace the equation with values listed in the Given. Solve the equation. • Phrase: Write the answer to the question in the form of a sentence. Given: v = 1.91 x 108 m/s c = 3.00 x 108 m/s Required: n Recall GRASP • Given: List the information given to you using symbols and numbers. Include units. • Required: List the item that needs to be solved. Use symbols. • Analysis: Write mathematical equation(s) that will be used. • Solution: Replace the equation with values listed in the Given. Solve the equation. • Phrase: Write the answer to the question in the form of a sentence. Given: v = 1.91 x 108 m/s c = 3.00 x 108 m/s Required: n Analysis: Solution: n= c v = 3.00 x 108 m/s = 1.57 1.91 x 108 m/s Recall GRASP • Given: List the information given to you using symbols and numbers. Include units. • Required: List the item that needs to be solved. Use symbols. • Analysis: Write mathematical equation(s) that will be used. • Solution: Replace the equation with values listed in the Given. Solve the equation. • Phrase: Write the answer to the question in the form of a sentence. Given: v = 1.91 x 108 m/s (glass) c = 3.00 x 108 m/s Required: n (glass) Analysis: Solution: n= c v = 3.00 x 108 m/s = 1.57 1.91 x 108 m/s Paraphrase: The refractive index of glass is 1.57 Given: n = 1.33 c = 3.00 x 108 m/s Required: v (water) Analysis: n = c , therefore v = c . v n Solution: v = 3.00 x108 m/s = 2.26 x 108 m/s 1.33 Paraphrase: The speed of light in water is 2.26 x 108 m/s Snell’s Law The index of refraction can also be calculated using sines of angles (trigonometry) n1 sine i = n2 sine R i is the angle of incidence R is the angle of refraction Actually written as: n1 sinθ 1 = n2 sinθ 2 A light ray moves from water to glass. The angle of incidence in water is 260. Calculate the refracted angle given the index of refraction for water is 1.33 and glass is 2.04. Given: θ1 = 26o, n 1 = 1.33, n2 = 2.04 Required: θ2 Analysis: n1 sinθ1 = n2 sinθ2 therefore n1 sinθ1 = sinθ2 n2 Solution: sinθ2 = 1.33 x sin 26o = 0.497 2.04 θ2 = sin-1 0.497 = 16.6o Phrase: The refracted angle of a light ray moving from water to glass is 16.6o Given the diagram below, calculate the angle of refraction and draw the refracted ray. Glass n = 1.52 Water n = 1.33 • Step 1: draw the normal • Step 2: measure the angle of incidence • Step 3: calculate the angle of refraction using Snell’s Law • Step 4: Draw the refracted ray using the angle calculated in step 3