1. PHYS219 Fall semester 2014 Lecture 21: Refraction of Electromagnetic Radiation: Lenses and Images Formed by Lenses Dimitrios Giannios Purdue University

2. Midtem II results average of all scores: 54.6%

3. Interaction of EM radiation with matter I(W/m 2 ) = R + T + A (conservation of energy) Three regimes: if R  I, mirrors if A  I, filters and absorbers if T  I, lenses EM radiation (light) travels slower in a material: n=c/v n - refractive index c= speed of light in vacuum (air) v=speed of light in a material a) b) I T R A materialn glass1.5 water1.33 diamond2.4

4. Refraction is the change in direction of light as it passes from one material to another. The change in direction is caused by a change in the speed of light in one material compared to the other. The index of refraction (n) is a measure of the speed of light in the material. Definition

5. n is always greater than 1 The index of refraction (n) has been measured for many, many materials

6. When light goes from one material to another, the frequency remains constant velocity = λf If light has a wavelength of 550 nm in air, what is the wavelength in water?

7. Snell’s Law (1621) * (no refraction when θ i = θ r = 0) * First reported by Ibn Sahl, Baghdad – 984 AD n 1 sin (θ i ) = n 2 sin(θ r )

8. Θ i =35 ◦ n 1 sin(Θ i ) = n 2 sin(Θ r ) 0.574 = 1.61sin Θ r sin(Θ r) = 0.356 Θ = 20.9 o 1.00sin(35 ) = 1.61sin Θ r Θ r =? n air =1.00 n glass =1.61 air flint glass Example II: n=1.33 n=1.51n=2.42 Examples Example I:

9. The case when n 1 > n 2 Total internal reflection: the critical angle n 1 sin(  i )=n 2 sin (  r ) When Θ i = Θ c, then Θ r = 90 ◦ n 1 sin(  c )= n 2 sin(90 ◦ )= n 2 Total internal reflection occurs when Θ i > Θ c

10. magnification Lightis refracted when passing through a transparent lens: image production

11. Two Different Classes of Lenses MirrorsLenses Concave Mirror Converging Lens Convex Mirror Diverging Lens

12. Converging Lens: A Systematic Summary Case 1 Case 2 Case 3 Case 4 Case 5 http://www.physicsclassroom.com

13. http://www.physicsclassroom.com/shwave/lenses Run Simulations

14. Diverging Lens: A Systematic Summary image locations Object locations

15. Sign Conventions are Important (different textbooks may use different conventions) Be able to distinguish between Real and Virtual Images *each symbol can be assigned either a + or - value QuantitySymbol*Positive Sign meansNegative Sign means Focal LengthfConverging LensDiverging Lens Object Distancesoso Object side of lens (real) Behind lens (virtual) Image Distancesisi Opposite side from object (real) Same side as object (virtual) MagnificationmImage uprightImage inverted Image Heighthihi Image uprightImage inverted Lenses

16. A 6.0-cm tall candle is placed a distance of 7.0 cm from a converging lens having a focal length of 16.0 cm. Determine the image distance and the image size. What we know: h o =6.0 cm s o =7.0 cm f=16.0 cm Virtual image Five Cases – which one applies? Upright image EXAMPLE I

17. What we know: h o =2.5 cm s o =40.0 cm f=-15.0 cm Virtual image Upright image A 2.5-cm tall nail is placed a distance of 40.0 cm from a diverging lens having a focal length of -15.0 cm. Determine the image distance and the image size. Example II