Refraction

1. Refraction

2. Air qA Water qw refraction Refraction Refraction is the bending of light as it passes from one medium into another. N Note: the angle of incidence qAin air and the angle of refraction qAin water are each measured with the normal N. The incident and refracted rays lie in the same plane and are reversible.

3. Air Air Water Water Refraction Distorts Vision The eye, believing that light travels in straight lines, sees objects closer to the surface due to refraction. Such distortions are common.

4. c Index of refraction v The Index of Refraction The index of refraction for a material is the ratio of the velocity of light in a vacuum (3 x 108 m/s) to the velocity through the material. Examples: Air n= 1; glass n = 1.5; Water n = 1.33

5. vair= c Air Glass n = 1.50 For glass: vG= 2 x 108 m/s Example 1. Light travels from air (n = 1) into glass, where its velocity reduces to only 2 x 108 m/s.What is the index of refraction for glass? If the medium were water: nW = 1.33. Then you should show that the velocity in water would be reduced from c to 2.26 x 108 m/s.

6. Pavement Air Glass Sand Analogy for Refraction 3 x 108 m/s 2 x 108 m/s vs < vp 3 x 108 m/s Light bends into glass then returns along original path much as a rolling axle would when encountering a strip of mud.

7. v1 Medium 1 v1t R q1 q2 q1 q1 v2t v2 q2 q2 Medium 2 Deriving Snell’s Law Consider two light rays. Velocities are v1in medium 1 and v2in med. 2. Segment R is common hypotenuse to two rgt. triangles. Verify shown angles from geometry.

8. Medium 1 q1 v1 v2 q2 Medium 2 Snell’s Law: Snell’s Law The ratio of the sine of the angle of incidence q1 to the sine of the angle of refraction q2 is equal to the ratio of the incident velocity v1to the refracted velocity v2 .

9. Air 300 H2O qW Example 2:A laser beam in a darkened room strikes the surface of water at an angle of 300. The velocity in water is 2.26 x 108 m/s. What is the angle of refraction? The incident angle is: qA qA = 900 – 300 = 600 qW = 40.70

10. Medium 1 q1 q2 Medium 2 Snell’s Law and Refractive Index Another form of Snell’s law can be derived from the definition of the index of refraction: Snell’s law for velocities and indices:

11. A Simplified Form of the Law Since the indices of refraction for many common substances are usually available, Snell’s law is often written in the following manner: The product of the index of refraction and the sine of the angle is the same in the refracted medium as for the incident medium.

12. Air Glass q qG 500 n=1.5 Air qe = 500 Apply to each interface: Same as entrance angle! Example 3. Light travels through a block of glass, then remerges into air. Find angle of emergence for given information. First find qG inside glass: qG qG = 30.70 From geometry, note angle qG same for next interface.

13. Air n=1 Glass n=1.5 lA lG Wavelength and Refraction The energy of light is determined by the frequency of the EM waves, which remains constant as light passes into and out of a medium. (Recall v = fl.) fA= fG lG < lA

14. The Many Forms of Snell’s Law: Refraction is affected by the index of refraction, the velocity, and the wavelength. In general: Snell’s Law: All the ratios are equal. It is helpful to recognize that only the index n differs in the ratio order.

15. Air Glass q qG qG n=1.5 q Air Example 4: A helium neon laser emits a beam of wavelength 632 nm in air (nA = 1). What is the wavelength inside a slab of glass (nG = 1.5)? nG = 1.5; lA = 632 nm Note that the light, if seen inside the glass, would be blue. Of course it still appears red because it returns to air before striking the eye.

16. Red Orange Yellow Green Blue Indigo Violet Dispersion by a Prism Dispersion is the separation of white light into its various spectral components. The colors are refracted at different angles due to the different indexes of refraction.

17. Air 900 qc Critical angle Water light Total Internal Reflection When light passes at an angle from a medium of higher index to one of lower index, the emerging ray bends away from the normal. When the angle reaches a certain maximum, it will be reflected internally. The critical angle qc is the limiting angle of incidence in a denser medium that results in an angle of refraction equal to 900. i = r

18. Critical angle Air 900 qc Critical angle: qc = 48.60 Water Example 5.Find the critical angle of incidence from water to air. For critical angle, qA = 900 nA= 1.0; nW = 1.33 In general, for media where n1 < n2 we find that:

19. c = 3 x 108 m/s Medium n v Index of refraction Snell’s Law: Summary Refraction is affected by the index of refraction, the velocity, and the wavelength. In general:

20. Critical angle n2 qc n1 900 n1 > n2 In general, for media where n1 > n2 we find that: Summary (Cont.) The critical angle qc is the limiting angle of incidence in a denser medium that results in an angle of refraction equal to 900.

21. c = 3 x 108 m/s Medium (n) v Index of refraction In general, for media where n1 > n2 we find that: Refraction Formulas Total Internal Reflection

22. The grating equation: d = slit width (spacing) q= angular deviation Bright fringes: Dark fringes: l= wavelength of light n = order of fringe Diffraction Formulas Young’s Experiment: Interference from a single slit of width a:

23. so R ho hi f si Reflection Summary The following equations apply equally well for both converging and diverging mirrors.

24. 1. Object distance so is positive for real objects and negative for virtual objects. Reflection: Sign Convention 2. Image distance si is positive for real images and negative for virtual images. 3. The focal length f and the radius of curvature R is positive for converging mirrors and negative for diverging mirrors. 4. The image height hi and the magnification M of images is positive for erect images and negative for inverted images.

25. Magnification: Obj. Obj. Img. Img. ho hi ho hi M = +2 M = -1/2 ho and hi are positive when erect; negative inverted. Reflection: Magnification The magnification M of an image is the ratio of the image size hi to the object size ho. si is positive when real; negative when virtual. M is positive when image erect; negative inverted.