Chapter 11.pdf

Snell’s LawThe phenomenon of refraction had been observed for centuries, but itwas not until 1621 that its cause was stated mathematically. WillebrordSnell (1591–1626) was a Dutch astronomer and mathematician who iscredited with identifying the exact relationship between the angle ofincidence and the angle of refraction.Snell’s law is a formula that uses values for the index of refractionto calculate the new angle that a ray will take as a beam of light strikesthe interface between two media (Figure 11.38). If you call the indicesof refraction of the two media n 1and n 2and call the angles of incidenceand the angle of refraction θ 1and θ 2, then the formula for Snell’s law is:interfacenormaln 1n 2 1 2441n 1sinθ 1= n 2sinθ 2Example Problem 11.7Figure 11.38 Snell’s law relates theindices of refraction with the angle ofincidence and the angle of refraction.When light passes from air into water at an angle of 60° from thenormal, what is the angle of refraction?GivenIndex of refraction of air n 1= 1.00Index of refraction of water n 2= 1.33Angle of incidence θ 1= 60°RequiredAngle of refraction = θ 2Analysis and SolutionThe correct equation is n 1sinθ 1= n 2sinθ 2n 1sinθ 1Manipulate it to solve for the variable needed sinθ 2=n 2Identify air as medium 1 and water as medium 2.Substitute the values and their units, and solve the problem.n 1sinθ 1sinθ 2=n 2=1.00 sin(60°)1.331.00 0.8660=1.33= 0.6511Therefore, θ 2= 40.62°ParaphraseThe angle of refraction is 41°.Practice Problems1. When light passes from airinto water at an angle of30° from the normal, whatis the angle of refraction?2. When light passes fromwater into diamond at anangle of 45° from thenormal, what is the angleof refraction?3. The refractive index of thelens in a human eye is1.41. If a ray of light goesfrom the air into the lensat an angle of 55.0°, whatis the angle of refraction?Ray diagrams model the behaviour of light in mirrors and lenses.