Refraction of Light and Thin Lenses

1. Chapter 15 Refraction

2. Section 15.1 - Refraction Objectives: Recognize situations in which refraction will occur Identify which direction light will bend when it passes from one medium to another Solve problems using Snell’s Law

3. Refraction of Light • Refraction is the bending of a wave disturbance as it passes (at an angle) from one medium into another • Refraction occurs because the velocity of light changes from one media to another • The speed of light decreases with the density of the medium

4. Refraction When light passes from a region of higher velocity (less dense medium) to a region of lower velocity, it will bend toward the normal. Air Water So, the angle of incidence is greater than the angle of refraction.

5. Just the opposite is true if light travels from a more dense material into a less dense material. Here the incident beam is starting through glass at an incident angle of i. When it reaches the glass/air boundary, it bends away from the normal, so the refracted angle, r, is greater than i.

6. There is no refraction at all if the incident ray is normal to the surface/boundary. Air 90o Water

7. For each of the diagrams below, which layer is more dense, and which is less dense? First, let’s show our normal lines so we can better compare incident (I) and refracted (R) angles… more dense less dense more dense I I I R R more dense less dense less dense R

8. Index of Refraction: • Ratio of the speed of light in a vacuum to the speed of light in a different medium n = index of refraction c = speed of light (vacuum) v = speed of light (other medium) • This can also be expressed in terms of wavelength o = wavelength of light (vacuum) n = wavelength of light (other medium)

9. Refraction of Light Each different medium has it’s own index of refraction, n. “Faster” mediums have lower values of n. n1 So, if we say air has n=n1 and water has n=n2, which is greater, n1 or n2? n2 n2 > n1

10. Refraction of Light Snell’s Law gives us a relationship between index of refraction and incident/refracted angles: ni(sin θi) = nr(sin θr) • ni is index of refraction for the material the • incident beam passes through • θi is incident angle • nr is index of refraction for the material the • refracted beam passes through • θr is the refracted angle

11. Snell’s Law Example A light ray of wavelength 589 nm (589x10-9 m) traveling through air strikes a smooth, flat slab of crown glass at an angle of 30o to the normal. What is the angle of refraction, θr ? ni(sin θi) = nr(sin θr) Incident angle? air Incident material? 30o Refracted material? crown glass Look at Table 15-1 on page 564 to get index of refractions for air and crown glass θr = 19.2o

12. Due to refraction, objects can appear to be in positions different than where they really are…. θi θr Where he sees it Where it is

13. Refraction of Light

14. Objectives: • Use ray diagrams to find the positions of images produced by converging or diverging lenses, and identify the images as real or virtual • Solve problems using the thin lens equation • Calculate the magnification of lenses • Describe the positioning of lenses in compound microscopes and refracting telescopes Section 15.2 – Thin Lenses

15. Lenses What is a lens? a transparent object that refracts light rays, causing them to converge or diverge to create an image The curved surfaces change the direction of light – refraction occurs at each surface (front/back)

16. Types of Lenses Converging Lenses (Convex) – thicker in center Diverging Lenses (Concave) – thinner in center

17. Types of Lenses - Continued Combination Lenses

18. Converging Lens Ray Diagrams – 3 Rays Parallel Ray: is incident parallel to principal axis; refracts through to focal point Central Ray: incident through center of lens; travels straight through lens Focal Ray: incident through the focal point; refracts parallel to principal axis Keep in mind….the light rays are not reflecting off the lenses like for mirrors. They are passing through and getting “bent”….they are refracting.

19. Ray Diagram – Converging Lens Note: focal points on both sides of the lens! We call the principal ray the “parallel ray” Is this image real or virtual???

20. Image Location for a Converging Lens Note distance verbage (p, q, f) and Image/Object Identification

21. Diverging Lens Ray Drawings – 3 Rays Parallel Ray: is incident parallel to principal axis; refracts away from focal point (refracted ray drawn backward to focal point) Central Ray: incident through center of lens; travels straight through lens Focal Ray: incident on a line that would go through the focal point; refracts parallel to principal axis (refracted ray drawn backward parallel to principal axis)

22. Image Location for a Diverging Lens Is this image real or virtual???

23. Thin-Lens Equation and Magnification object distance image distance focal length p = ? q = ? f = ? Magnification image height object height M = ? h’ = ? h = ?

24. Thin Lens Equation • The object distance, p, is always positive • The image distance, q, is negative if the image • is on the same side of the lens as the object • The focal length for a converging lens is positive • The focal length of a diverging lens is negative

25. Thin Lens Equation Examples An object is placed 30.0cm in front of a converging lens of focal length 10.0cm. * Calculate the image distance * Calculate the magnification * Describe the image - Upright or inverted? - Bigger or smaller? - Front side or back side of lens? - Real or virtual? ANS: q=15.0cm M = -0.5 Inverted, smaller, back side, real

26. Thin Lens Equation Examples An object is placed 312.5cm in front of a diverging lens of focal length 10.0cm. * Calculate the image distance * Calculate the magnification * Describe the image - Upright or inverted? - Bigger or smaller? - Front side or back side of lens? - Real or virtual? ANS: q=-5.55cm M = 0.444 Upright, smaller, front side, virtual

27. Thin Lens Combinations The image from lens1 becomes the object for lens2 p2 p1 q1 q2

28. Section 15.3 – Optical Phenomena Objectives: Predict whether light will be refracted or undergo total internal reflection Recognize atmospheric conditions that cause refraction Explain dispersion, and phenomena such as rainbows in terms of the relationship between index of refraction and wavelength

29. Total Internal Reflection Total internal reflection is the complete reflection of light at the boundary between two transparent media. It occurs when the angle of incidence exceeds the critical angle.

30. Total Internal Reflection

31. Snell’s Law and Total Internal Reflection The critical angle (of incidence) occurs when the angle of refraction is 90o (and sin 90o = 1)

32. Total Internal Reflection - example Find the critical angle for light traveling from glycerine (n=1.473) into air. θc = 42.8o

33. Total Internal Reflection - Applications • Diamonds – are cut in a way to allow for much total internal reflection, and the light that refracts out of a diamond to make it “shine” exits from just the faces the most visible faces of the diamond • Fiber Optics – using very thin glass or plastic fibers allows for light to be internally reflected over and over again within the fibers. Bundling these fibers into small cables can allow for viewing images in otherwise inaccessible locations.

34. Atmospheric Refraction Bending of light rays due to temperature differences

35. Atmospheric Refraction

36. Atmospheric Refraction

37. Atmospheric Refraction

38. Dispersion The process of separating polychromatic light into its separate wavelengths

39. Dispersion

40. Lens Aberrations Chromatic Aberration: The focusing of different wavelengths of light at different distances behind a lens

41. Lens Aberrations Spherical Aberration: incident light rays far from the principal axis don’t refract through the focal point This image would be sharp This image would be blurry