Refraction: Snell's Law October 26, 2010
When light passes from one medium into another, part of the incident light is reflected at the boundary The remainder passes into the new medium. Unless it is perpendicular, the ray will bend. (like a pencil in a beaker of water) This is called refraction
Why? Speed of light in a vacuum is close to the speed of light in air because light offers very little resistance. However: when light travels through water, for example, it slows down.
The light bends toward the normal when it goes from a medium that slows light waves down (more dense)
Index of Refraction ratio between the speed of light in a n = c vacuum and speed of light in a v trasparent medium c = speed of light in a vacuum v = speed of light in a medium n = index of refraction (the ratio)
Table of indices of Refraction page 61 of old text Example: Speed of light in a liquid is 2.25 x 10 8 m/s. What is the a) refractive index of the liquid? a) c = 3.00 x 10 8 m/s, v = 2.25 x 10 8 m/s Formula: n = c/v Calculation: n = 3.00 x 10 8 m/s/2.25 x 10 8 m/s = 1.33 b) look on page 61 of text, what is the liquid according to the table of indices of Refraction?
When the index of refraction refers light passing between two transparent media relative index of refraction (n 1 2 = n 2 n 1 = n 2 /n 1 )
Laws of Refraction: Sin i Sin R = n Example: The angle of incidence is 30.0 o and the angle of refraction is 24.0 o. Calculate the index of refraction of the unknown medium. sin 30 o sin 24 o = n n = 0.500/0.407 = 1.23
Java applet for refraction and reflection http://lectureonline.cl.msu.edu/~mmp/kap25/snell/app.htm
Snell's law is written n 1 sin i = n 2 sin R n 1 is the index of refraction for the first medium n 2 is the index of refraction for the second medium
Use subscripts to indicate the different mediums. Example Light travels from crown glass (g) into water (w). The angle of incidence in crown glass is 40.0 o. What is the angle of refraction in water? (use the table to get indices of refraction p.61) n g sin g = n w sin R 1.52 sin 40.0 o = 1.33 sin R sin w = (1.52)(0.643)/1.33 = 0.735 w = Sin -1 (0.735) w = 47.3 o
Total Internal Reflection and the Critical Angle As the angle of incidence increases, the intensity of a reflected ray becomes progressively stronger. And... intensity of a refracted ray becomes progressively weaker. θ R θi θr
Total internal reflection - occurs when light is leaving a denser medium and is travelling into a less dense medium and θ i > the critical angle. N
Total internal reflection The critical angle is a constant between two media. - occurs when light is leaving a denser medium It and is the is value travelling of θ into when a less θ = dense 90 o medium and i R θ i > the critical angle. a) θ i < the critcial angle : a refracted ray (partial reflection). b) θ = the critical angle : critical ray of 90 o (to the normal). i c) θ i > the critical angle : totally reflected ray (no refraction)
To calculate the critical angle Total internal reflection for any substance set the angle of refraction to 90 o. - occurs when light is leaving a denser medium and is travelling into a less dense medium and Example: The light ray is travelling from diamond (n 1 = 2.42) to air (n 2 = 1.0003) n1sin ic = n2 sin R θ i > the critical angle. n 1 sinθ i = n 2 sinθ R 2.42 (sin θ i ) = 1.0003 ( sin 90 o ) 2.42 (sin θ i ) = 1.0003 (1.0) 2.42(sin θ i ) = 1.0003 sin θ i = 0.4133 θ i = sin -1 (0.4133) i = 24.4 o
Practice in textbook P. 78 79 # 16, 17, 23, 30, 36, 37, 38, 39, 40,42,45, 50 (3 mediums therefore 2 steps) Note the answers to many of the questions are in the back. y < -1/3x + 12 y < 2x y > 5 x < 9
Parabolic mirror: http://www.youtube.com/watch?v=ij1yvjt5tlq&feature=related Classroom demo: reflection and images: http://www.youtube.com/watch?v=myf47078iis&feature=related
Challenge of the week: Sherlock Holmes: case of the disappearing jewelry Suspect is believed to be planning a heist. You are hiding behind a desk, and have 3 flat mirrors set up to catch the thief in the act. Show how you might set them up in order to "see" the thief in action Facts: room is 8.5 x 11 (size of paper) the desk is in one corner and the table with the jewelry is on the other side of the desk you must use all 3 mirrors (hint: use laws of reflection, ruler and protractor)
today's challenge JELLO CHALLENGE Collecting data for index of refraction Hand in one table per group θi θr n =