Physics 1230: Light and Color Ivan I. Smalyukh, Instructor Office: Gamow Tower, F Phone: Lectures: Tuesdays & Thursdays, 3:30 PM - 4:45 PM Office hours: Mondays & Fridays, 3:30 PM – 4:30 PM TA: Jhih-An Yang Class # 7

2 Physics 1230: Light and Color Lecture 7: Reading: Finish reading Chapter 2 Demos

33 Lec. 6: Ch. 2 - Geometrical Optics 1.Shadows 2.Reflection 3.Refraction 4.Dispersion We are here

Reflection at transparent material interfaces Part of the wave can be transmitted into the second medium while part is reflected back When light waves are incident on a glass slab they are mostly transmitted but partly reflected (about 4%)! Glass slab Is the speed of light in the glass slab the same as in the free space??? No.

How can reflection require that the speed of the wave changes? c = 3 x 10 8 m/s! The speed of an electromagnetic (EM) wave is constant (for every wavelength) in empty space! The speed of light is slower than c in glass, water and other transparent media The speed of light in a medium is v = c/n, where n is a number larger than one called the index of refraction n = 1.5 for glass n = 1.3 for water n = 1.5 for vegetable oil Glass slab

Material Refractive Index Air Water1.330 Glass1.5 Diamond2.417 Ruby1.760 Oil1.5 Refractive indices of different materials Can we see a glass rod immersed into the oil with the same refractive index? A. Yes B. No Why?

7 Refraction 1.Index of refraction: n = c / v 2.Ray in water is closer to the normal 3.Total internal reflection 4.Rainbows, Mirages

8 What is refraction? Refraction is bending of a ray at a boundary due to a different speed of light in the substance. Air Water Air Water Demo: tank, laser pointer

The incident ray has peaks and troughs in the wave. The wave that hits the material first slows down. Causes the wave to bend. Just like waves hitting the shoreline. Analogy with car driving (twee wheels on a slippery part of the road) … Incident ray High index Higher index Why does the ray bend?

10 Why does the ray bend? Refraction is bending of a ray at a boundary due to a different speed of light in the substance. Air Water Air Water Demo: tank, laser pointer Towards or away from the interface

11 Indices of refraction Substance:Index of refraction n: Vacuum … Air Water1.333 Glass1.5 (depends on kind) Diamond2.4 v = c / n

Clicker Question 12 A material with a larger index of refraction, n, has a: A)Faster speed of light B)Slower speed of light C)Depends upon the particular material. Recall: v = c / n

13 Snell’s law n 1 sin  1 = n 2 sin  2 Air Water n 2 = 1.33 n 1 = 11 22

Refraction - bending of a ray after it enters a medium where its speed is different A ray going from a fast medium to a slow medium bends towards the normal A ray going from a slow to a fast medium bends away from the normal Hence, a ray going into a medium with a higher n bends towards the normal & a ray going into a medium with a lower n bends away from the normal Air (fast medium) Glass or water (slow) Normal Glass or water (slow) Normal Air (fast medium) n air < n water < 1.33 How about light going into a medium with exactly the same n?

15 Light coming out of water: 2 possibilities Air Water Refracted Reflected internally Case 1 near normal incidence (light comes out) Case 2, far from normal incidence (internal reflection) Demo: tank, laser pointer The critical angle is about 42 degrees. Refraction out OR Total internal reflection!

Total internal reflection Show that the internal reflection is a consequence of the Snell’s law The amount of bending is determined by the law of refraction (sometimes called Snell's law): n i sin  i = n t sin  t

Total internal reflection - extreme case of a ray bending away from the normal as it goes from higher to lower n Glass or water (slow) Normal Air (fast medium) Just below the critical angle for total internal reflection there is a reflected & a transmitted ray Glass or water (slow) Normal Above the critical angle for total internal reflection there is reflected ray but no transmitted ray Critical angle For the glass-air interface

Ray-bending & our psychological straight-ray interpretation incident ray transmitted ray normal image of fish for someone out of water fish To observe the fish from outside the water a transmitted ray must enter your eye You will think it comes from a point obtained by tracing it backwards, Extend any 2 of the many many transmitted rays from the fish backwards to find the image of the fish (where they intersect). The location of that image will be the same for any observer outside of the water.

What we see and how different it can be from what it seems to be The woman will see the underwater part of body being a)Smaller than it really is; b)Much larger than it really is; c)Of natural size; Two observers, one above the water and one under the water, view an object (fellow to the left)…

The woman will see the underwater part of body being a)Smaller than it really is; b)Much larger than it really is; c)Of natural size; What we see and how different it can be from what it seems to be

The boy will see the underwater part of body being a)Smaller than it really is; b)Much larger than it really is; c)Of natural size; d) Something else. Two observers, one above the water and one under the water, view an object (fellow to the left)…

What we see and how different it can be from what it seems to be If the critical angle condition is satisfied, will the boy see the upper part of the man’s body? a)Yes; b)No.

What we see and how different it can be from what it seems to be The boy will see the underwater part of body being a)Smaller than it really is; b)Much larger than it really is; c)Of natural size; d) Something else. Legs up and down!

24 Lec. 6: Ch. 2 - Geometrical Optics 1.Shadows 2.Reflection 3.Refraction 4.Dispersion We are here

25 Dispersion Dispersion: refraction (bending) of different colors by different amounts. Light bulbSpectrumPrism

26 Index n varies with color wavelengthn (index of refraction) 300 nm (UV)1.486 (bent more) 500 nm nm (deep red)1.455 (bent less) Quartz glass

Prisms demonstrate refraction and dispersion 27 Reflection at a transparent surface occurs because the n values are different. Only a few percent of the light is reflected this way.

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29 Rainbows: dispersion & by water raindrops 180 degree rainbow is possible. Double rainbow is possible. Both together is very rare.

30 How we see a rainbow big raindrops Sun (behind you) this ray not seen these rays are seen

Raindrop Dispersion occurs here during refraction white light comes in Reflections Dispersion occurs here during refraction A spectrum of colors comes out The colors are spread inside the prism as well as outside. The colors start to spread inside the raindrop.

32 How we see two rainbows sun two total internal reflections three total internal reflections

33 Waterfall droplets create rainbows

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35 Fogbow (sun behind you) (sun if front of you) 22 degrees, center to edge

36 What is a mirage? A mirage is an image (often upside down) caused by heated air refracting rays. n falls from at room temperature to when the temperature goes up 100 C.

37 Inferior mirage (image below the object) sky appears to be on the ground The ray bends from the low n material toward the high n material.

38 Superior mirage (image above the object)

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40 Sun pillar and sun dogs How do these work?

41 Total internal reflection makes fiber optic communication possible The ray bends from the low n material toward the high n material. Demo: glass tube, laser pointer

Time for a demo! 42 If we pull the cork, and water starts to pour out of the tank, the laser light will… A)Shine across the room to the wall. B)Stay entirely inside the tank C)Stay entirely inside the water stream D)Something else happens.

43 This illustration appears in "La Nature" magazine in Demo: tank

44 Lec. 6: Ch. 2 - Geometrical Optics 1.Shadows 2.Reflection 3.Refraction 4.Dispersion Move to Chap. 3 We are here