For more topics - see subject index of interactive diagrams.
Bending Light
If you have ever half-submerged a straight stick into water, you have probably noticed that the stick
appears bent at the point it enters the water (see Figure 1.) This optical effect is due to refraction. As light
passes from one transparent medium to another, it changes speed, and bends. How much this happens
depends on the refractive index of the mediums and the angle between the light ray and the line
perpendicular (normal) to the surface separating the two mediums (medium/medium interface) (See Figures 2a and 2b.) Each medium has a different refractive
index (see list below.) The angle between the light ray and the
normal as it leaves a medium is called the angle of incidence. The angle between the light ray and the normal
as it enters a medium is called the angle of refraction.
Snell's Law
In 1621, a Dutch physicist named Willebrord Snell (1591-1626), derived the relationship between the
different angles of light as it passes from one transperent medium to another.
When light passes from one transparent medium to another, it bends
according to Snell's law which states:
Ni * Sin(Ai) = Nr * Sin(Ar),
where: Ni is the refractive index of the medium the light is leaving, Ai is the incident angle between the light ray and the normal to the meduim to medium interface, Nr is the refractive index of the medium the light is entering, Ar is the refractive angle between the light ray and the normal to the meduim to medium interface.
Figure 3. Refraction simulator
You can experiment with effects of different incident angles and refractive indices with Figure 3. You can move the flashlight
around, and change the refractive index of the top and bottom mediums. You can use the
buttons to quickly enter the index for a few common mediums.
Critical Angle
Using the refraction simulator, notice how the light bends toward the normal when the light enters a medium of greater refractive index, and away from the normal when
entering a medium of lesser refractive index. Then notice what happens when you move the flashlight to an angle close to 90 or -90 degrees
in the medium with a higher refractive index. As you approach the critical angle the refracted light approaches 90 or -90 degrees
and, at the critical angle, the angle of refractions becomes 90 or -90 and the light is no longer transmitted across the medium/medium interface. For
angles greater in absolute value than the critical angle, all the light is reflected. This is called total internal reflection.
Related links
Click here to hear a song about refraction and Snell's Law by Marian McKenzie and Walter Fox Smith as performed by Russ and Eli.
Below are some other refractive indices to try. Are there
any that have a smaller index than a vacuum (1.0)?
Warning: These numbers
were not derived by me, nore can I claim they are accurate. Please use
these values for demonstration purposes in the simulation only.
Sorted by medium:
Acetone
1.36
Actinolite
1.618
Agalmatoite
1.550
Agate
1.544
Agate, Moss
1.540
Air
1.0002926
Alcohol
1.329
Alexandrite
1.745
Aluminum
1.44
Amber
1.546
Amblygonite
1.611
Amethyst
1.544
Anatase
2.490
Andalusite
1.641
Anhydrite
1.571
Apatite
1.632
Apophyllite
1.536
Aquamarine
1.577
Aragonite
1.530
Argon
1.000281
Asphalt
1.635
Augelite
1.574
Axinite
1.675
Azurite
1.730
Barite
1.636
Barytocalcite
1.684
Benitoite
1.757
Benzene
1.501
Beryl
1.577
Beryllonite
1.553
Brazilianite
1.603
Bromine (liq)
1.661
Bronze
1.18
Brownite
1.567
Calcite
1.486
Calspar
1.486
Cancrinite
1.491
Carbon Dioxide (gas)
1.000449
Carbon Disulfide
1.628
Carbon Tetrachloride
1.460
Cassiterite
1.997
Celestite
1.622
Cerussite
1.804
Ceylanite
1.770
Chalcedony
1.530
Chalk
1.510
Chalybite
1.630
Chlorine (gas)
1.000768
Chlorine (liq)
1.385
Chrome Green
2.4
Chrome Red
2.42
Chrome Yellow
2.31
Chromium
2.97
Chrysoberyl
1.745
Chrysocolla
1.500
Chrysoprase
1.534
Citrine
1.550
Clinozoisite
1.724
Cobalt Blue
1.74
Cobalt Green
1.97
Cobalt Violet
1.71
Colemanite
1.586
Copper
1.10
Copper Oxide
2.705
Coral
1.486
Cordierite
1.540
Corundum
1.766
Crocoite
2.310
Crystal
2.00
Cuprite
2.850
Danburite
1.633
Diamond
2.417
Diopside
1.680
Dolomite
1.503
Dumortierite
1.686
Ebonite
1.66
Ekanite
1.600
Elaeolite
1.532
Emerald
1.576
Emerald, Synth flux
1.561
Emerald, Synth hydro
1.568
Enstatite
1.663
Epidote
1.733
Ethanol
1.36
Ethyl Alcohol
1.36
Euclase
1.652
Fabulite
2.409
Feldspar, Adventurine
1.532
Feldspar, Albite
1.525
Feldspar, Amazonite
1.525
Feldspar, Labradorite
1.565
Feldspar, Microcline
1.525
Feldspar, Oligoclase
1.539
Feldspar, Orthoclase
1.525
Fluoride
1.56
Fluorite
1.434
Formica
1.47
Garnet, Almandine
1.760
Garnet, Almandite
1.790
Garnet, Andradite
1.820
Garnet, Demantoid
1.880
Garnet, Grossular
1.738
Garnet, Hessonite
1.745
Garnet, Rhodolite
1.760
Garnet, Spessartite
1.810
Gaylussite
1.517
Glass
1.51714
Glass, Albite
1.4890
Glass, Crown
1.520
Glass, Crown, Zinc
1.517
Glass, Flint, Dense
1.66
Glass, Flint, Heaviest
1.89
Glass, Flint, Heavy
1.65548
Glass, Flint, Lanthanum
1.80
Glass, Flint, Light
1.58038
Glass, Flint, Medium
1.62725
Glycerine
1.473
Gold
0.47
Hambergite
1.559
Hauynite
1.502
Helium
1.000036
Hematite
2.940
Hemimorphite
1.614
Hiddenite
1.655
Howlite
1.586
Hydrogen (gas)
1.000140
Hydrogen (liq)
1.0974
Hypersthene
1.670
Ice
1.309
Idocrase
1.713
Iodine Crystal
3.34
Iolite
1.548
Iron
1.51
Ivory
1.540
Jade, Nephrite
1.610
Jadeite
1.665
Jasper
1.540
Jet
1.660
Kornerupine
1.665
Kunzite
1.655
Kyanite
1.715
Lapis Gem
1.500
Lapis Lazuli
1.61
Lazulite
1.615
Lead
2.01
Leucite
1.509
Magnesite
1.515
Malachite
1.655
Meerschaum
1.530
Mercury (liq)
1.62
Methanol
1.329
Moldavite
1.500
Moonstone, Adularia
1.525
Moonstone, Albite
1.535
Natrolite
1.480
Nephrite
1.600
Nitrogen (gas)
1.000297
Nitrogen (liq)
1.2053
Nylon
1.53
Obsidian
1.489
Olivine
1.670
Onyx
1.486
Opal
1.450
Oxygen (gas)
1.000276
Oxygen (liq)
1.221
Painite
1.787
Pearl
1.530
Periclase
1.740
Peridot
1.654
Peristerite
1.525
Petalite
1.502
Phenakite
1.650
Phosgenite
2.117
Plastic
1.460
Plexiglas
1.50
Polystyrene
1.55
Prase
1.540
Prasiolite
1.540
Prehnite
1.610
Proustite
2.790
Purpurite
1.840
Pyrite
1.810
Pyrope
1.740
Quartz
1.544
Quartz, Fused
1.45843
Rhodizite
1.690
Rhodochrisite
1.600
Rhodonite
1.735
Rock Salt
1.544
Rubber, Natural
1.5191
Ruby
1.760
Rutile
2.62
Sanidine
1.522
Sapphire
1.760
Scapolite
1.540
Scapolite, Yellow
1.555
Scheelite
1.920
Selenium, Amorphous
2.92
Serpentine
1.560
Shell
1.530
Silicon
4.24
Sillimanite
1.658
Silver
0.18
Sinhalite
1.699
Smaragdite
1.608
Smithsonite
1.621
Sodalite
1.483
Sodium Chloride
1.544
Sphalerite
2.368
Sphene
1.885
Spinel
1.712
Spodumene
1.650
Staurolite
1.739
Steatite
1.539
Steel
2.50
Stichtite
1.520
Strontium Titanate
2.410
Styrofoam
1.595
Sulphur
1.960
Synthetic Spinel
1.730
Taaffeite
1.720
Tantalite
2.240
Tanzanite
1.691
Teflon
1.35
Thomsonite
1.530
Tiger eye
1.544
Topaz
1.620
Topaz, Blue
1.610
Topaz, Pink
1.620
Topaz, White
1.630
Topaz, Yellow
1.620
Tourmaline
1.624
Tremolite
1.600
Tugtupite
1.496
Turpentine
1.472
Turquoise
1.610
Ulexite
1.490
Uvarovite
1.870
Variscite
1.550
Vivianite
1.580
Wardite
1.590
Water (gas)
1.000261
Water 100'C
1.31819
Water 20'C
1.33335
Water 35'C (Room temp)
1.33157
Willemite
1.690
Witherite
1.532
Wulfenite
2.300
Zincite
2.010
Zircon, High
1.960
Zircon, Low
1.800
Zirconia, Cubic
2.170
Sorted by refractive index:
Silver
0.18
Gold
0.47
Helium
1.000036
Hydrogen (gas)
1.00014
Water (gas)
1.000261
Oxygen (gas)
1.000276
Argon
1.000281
Air
1.0002926
Nitrogen (gas)
1.000297
Carbon Dioxide (gas)
1.000449
Chlorine (gas)
1.000768
Hydrogen (liq)
1.0974
Copper
1.1
Bronze
1.18
Nitrogen (liq)
1.2053
Oxygen (liq)
1.221
Ice
1.309
Water 100'C
1.31819
Alcohol
1.329
Methanol
1.329
Water 35'C (Room temp)
1.33157
Water 20'C
1.33335
Teflon
1.35
Acetone
1.36
Ethanol
1.36
Ethyl Alcohol
1.36
Chlorine (liq)
1.385
Fluorite
1.434
Aluminum
1.44
Opal
1.45
Quartz, Fused
1.45843
Carbon Tetrachloride
1.46
Plastic
1.46
Formica
1.47
Turpentine
1.472
Glycerine
1.473
Natrolite
1.48
Sodalite
1.483
Calcite
1.486
Calspar
1.486
Coral
1.486
Onyx
1.486
Glass, Albite
1.489
Obsidian
1.489
Ulexite
1.49
Cancrinite
1.491
Tugtupite
1.496
Chrysocolla
1.5
Lapis Gem
1.5
Moldavite
1.5
Plexiglas
1.5
Benzene
1.501
Hauynite
1.502
Petalite
1.502
Dolomite
1.503
Leucite
1.509
Chalk
1.51
Iron
1.51
Magnesite
1.515
Gaylussite
1.517
Glass, Crown, Zinc
1.517
Glass
1.51714
Rubber, Natural
1.5191
Glass, Crown
1.52
Stichtite
1.52
Sanidine
1.522
Feldspar, Albite
1.525
Feldspar, Amazonite
1.525
Feldspar, Microcline
1.525
Feldspar, Orthoclase
1.525
Moonstone, Adularia
1.525
Peristerite
1.525
Aragonite
1.53
Chalcedony
1.53
Meerschaum
1.53
Nylon
1.53
Pearl
1.53
Shell
1.53
Thomsonite
1.53
Elaeolite
1.532
Feldspar, Adventurine
1.532
Witherite
1.532
Chrysoprase
1.534
Moonstone, Albite
1.535
Apophyllite
1.536
Feldspar, Oligoclase
1.539
Steatite
1.539
Agate, Moss
1.54
Cordierite
1.54
Ivory
1.54
Jasper
1.54
Prase
1.54
Prasiolite
1.54
Scapolite
1.54
Agate
1.544
Amethyst
1.544
Quartz
1.544
Rock Salt
1.544
Sodium Chloride
1.544
Tiger eye
1.544
Amber
1.546
Iolite
1.548
Agalmatoite
1.55
Citrine
1.55
Polystyrene
1.55
Variscite
1.55
Beryllonite
1.553
Scapolite, Yellow
1.555
Hambergite
1.559
Fluoride
1.56
Serpentine
1.56
Emerald, Synth flux
1.561
Feldspar, Labradorite
1.565
Brownite
1.567
Emerald, Synth hydro
1.568
Anhydrite
1.571
Augelite
1.574
Emerald
1.576
Aquamarine
1.577
Beryl
1.577
Vivianite
1.58
Glass, Flint, Light
1.58038
Colemanite
1.586
Howlite
1.586
Wardite
1.59
Styrofoam
1.595
Ekanite
1.6
Nephrite
1.6
Rhodochrisite
1.6
Tremolite
1.6
Brazilianite
1.603
Smaragdite
1.608
Jade, Nephrite
1.61
Lapis Lazuli
1.61
Prehnite
1.61
Topaz, Blue
1.61
Turquoise
1.61
Amblygonite
1.611
Hemimorphite
1.614
Lazulite
1.615
Actinolite
1.618
Mercury (liq)
1.62
Topaz
1.62
Topaz, Pink
1.62
Topaz, Yellow
1.62
Smithsonite
1.621
Celestite
1.622
Tourmaline
1.624
Glass, Flint, Medium
1.62725
Carbon Disulfide
1.628
Chalybite
1.63
Topaz, White
1.63
Apatite
1.632
Danburite
1.633
Asphalt
1.635
Barite
1.636
Andalusite
1.641
Phenakite
1.65
Spodumene
1.65
Euclase
1.652
Peridot
1.654
Hiddenite
1.655
Kunzite
1.655
Malachite
1.655
Glass, Flint, Heavy
1.65548
Sillimanite
1.658
Ebonite
1.66
Glass, Flint, Dense
1.66
Jet
1.66
Bromine (liq)
1.661
Enstatite
1.663
Jadeite
1.665
Kornerupine
1.665
Hypersthene
1.67
Olivine
1.67
Axinite
1.675
Diopside
1.68
Barytocalcite
1.684
Dumortierite
1.686
Rhodizite
1.69
Willemite
1.69
Tanzanite
1.691
Sinhalite
1.699
Cobalt Violet
1.71
Spinel
1.712
Idocrase
1.713
Kyanite
1.715
Taaffeite
1.72
Clinozoisite
1.724
Azurite
1.73
Synthetic Spinel
1.73
Epidote
1.733
Rhodonite
1.735
Silver
0.18
Gold
0.47
Helium
1.000036
Hydrogen (gas)
1.00014
Water (gas)
1.000261
Oxygen (gas)
1.000276
Argon
1.000281
Air
1.0002926
Nitrogen (gas)
1.000297
Carbon Dioxide (gas)
1.000449
Chlorine (gas)
1.000768
Hydrogen (liq)
1.0974
Copper
1.1
Bronze
1.18
Nitrogen (liq)
1.2053
Oxygen (liq)
1.221
Ice
1.309
Water 100'C
1.31819
Alcohol
1.329
Methanol
1.329
Water 35'C (Room temp)
1.33157
Water 20'C
1.33335
Teflon
1.35
Acetone
1.36
Ethanol
1.36
Ethyl Alcohol
1.36
Chlorine (liq)
1.385
Fluorite
1.434
Aluminum
1.44
Opal
1.45
Quartz, Fused
1.45843
Carbon Tetrachloride
1.46
Plastic
1.46
Formica
1.47
Turpentine
1.472
Glycerine
1.473
Natrolite
1.48
Sodalite
1.483
Calcite
1.486
Calspar
1.486
Coral
1.486
Onyx
1.486
Glass, Albite
1.489
Obsidian
1.489
Ulexite
1.49
Cancrinite
1.491
Tugtupite
1.496
Chrysocolla
1.5
Lapis Gem
1.5
Moldavite
1.5
Plexiglas
1.5
Benzene
1.501
Hauynite
1.502
Petalite
1.502
Dolomite
1.503
Leucite
1.509
Chalk
1.51
Iron
1.51
Magnesite
1.515
Gaylussite
1.517
Glass, Crown, Zinc
1.517
Glass
1.51714
Rubber, Natural
1.5191
Glass, Crown
1.52
Stichtite
1.52
Sanidine
1.522
Feldspar, Albite
1.525
Feldspar, Amazonite
1.525
Feldspar, Microcline
1.525
Feldspar, Orthoclase
1.525
Moonstone, Adularia
1.525
Peristerite
1.525
Aragonite
1.53
Chalcedony
1.53
Meerschaum
1.53
Nylon
1.53
Pearl
1.53
Shell
1.53
Thomsonite
1.53
Elaeolite
1.532
Feldspar, Adventurine
1.532
Witherite
1.532
Chrysoprase
1.534
Moonstone, Albite
1.535
Apophyllite
1.536
Feldspar, Oligoclase
1.539
Steatite
1.539
Agate, Moss
1.54
Cordierite
1.54
Ivory
1.54
Jasper
1.54
Prase
1.54
Prasiolite
1.54
Scapolite
1.54
Agate
1.544
Amethyst
1.544
Quartz
1.544
Rock Salt
1.544
Sodium Chloride
1.544
Tiger eye
1.544
Amber
1.546
Iolite
1.548
Agalmatoite
1.55
Citrine
1.55
Polystyrene
1.55
Variscite
1.55
Beryllonite
1.553
Scapolite, Yellow
1.555
Hambergite
1.559
Fluoride
1.56
Serpentine
1.56
Emerald, Synth flux
1.561
Feldspar, Labradorite
1.565
Brownite
1.567
Emerald, Synth hydro
1.568
Anhydrite
1.571
Augelite
1.574
Emerald
1.576
Aquamarine
1.577
Beryl
1.577
Vivianite
1.58
Glass, Flint, Light
1.58038
Colemanite
1.586
Howlite
1.586
Wardite
1.59
Styrofoam
1.595
Ekanite
1.6
Nephrite
1.6
Rhodochrisite
1.6
Tremolite
1.6
Brazilianite
1.603
Smaragdite
1.608
Jade, Nephrite
1.61
Lapis Lazuli
1.61
Prehnite
1.61
Topaz, Blue
1.61
Turquoise
1.61
Amblygonite
1.611
Hemimorphite
1.614
Lazulite
1.615
Actinolite
1.618
Mercury (liq)
1.62
Topaz
1.62
Topaz, Pink
1.62
Topaz, Yellow
1.62
Smithsonite
1.621
Celestite
1.622
Tourmaline
1.624
Glass, Flint, Medium
1.62725
Carbon Disulfide
1.628
Chalybite
1.63
Topaz, White
1.63
Apatite
1.632
Danburite
1.633
Asphalt
1.635
Barite
1.636
Andalusite
1.641
Phenakite
1.65
Spodumene
1.65
Euclase
1.652
Peridot
1.654
Hiddenite
1.655
Kunzite
1.655
Malachite
1.655
Glass, Flint, Heavy
1.65548
Sillimanite
1.658
Ebonite
1.66
Glass, Flint, Dense
1.66
Jet
1.66
Bromine (liq)
1.661
Enstatite
1.663
Jadeite
1.665
Kornerupine
1.665
Hypersthene
1.67
Olivine
1.67
Axinite
1.675
Diopside
1.68
Barytocalcite
1.684
Dumortierite
1.686
Rhodizite
1.69
Willemite
1.69
Tanzanite
1.691
Sinhalite
1.699
Cobalt Violet
1.71
Spinel
1.712
Idocrase
1.713
Kyanite
1.715
Taaffeite
1.72
Clinozoisite
1.724
Azurite
1.73
Synthetic Spinel
1.73
Epidote
1.733
Rhodonite
1.735
Garnet, Grossular
1.738
Staurolite
1.739
Cobalt Blue
1.74
Periclase
1.74
Pyrope
1.74
Alexandrite
1.745
Chrysoberyl
1.745
Garnet, Hessonite
1.745
Benitoite
1.757
Garnet, Almandine
1.76
Garnet, Rhodolite
1.76
Ruby
1.76
Sapphire
1.76
Corundum
1.766
Ceylanite
1.77
Painite
1.787
Garnet, Almandite
1.79
Glass, Flint, Lanthanum
1.8
Zircon, Low
1.8
Cerussite
1.804
Garnet, Spessartite
1.81
Pyrite
1.81
Garnet, Andradite
1.82
Purpurite
1.84
Uvarovite
1.87
Garnet, Demantoid
1.88
Sphene
1.885
Glass, Flint, Heaviest
1.89
Scheelite
1.92
Sulphur
1.96
Zircon, High
1.96
Cobalt Green
1.97
Cassiterite
1.997
Crystal
2
Lead
2.01
Zincite
2.01
Phosgenite
2.117
Zirconia, Cubic
2.17
Tantalite
2.24
Wulfenite
2.3
Chrome Yellow
2.31
Crocoite
2.31
Sphalerite
2.368
Chrome Green
2.4
Fabulite
2.409
Strontium Titanate
2.41
Diamond
2.417
Chrome Red
2.42
Anatase
2.49
Steel
2.5
Rutile
2.62
Copper Oxide
2.705
Proustite
2.79
Cuprite
2.85
Selenium, Amorphous
2.92
Hematite
2.94
Chromium
2.97
Iodine Crystal
3.34
Silicon
4.24
Figure 1. Optical effect of refraction.
Figure 2a. Angles of Incidence and Refraction (2D).
Figure 2b. Angles of Incidence and Refraction (3D).
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