Refractive Index Calculator - Find n and Identify a Material

Refractive index, found three ways

Two angles from a laser and a protractor, the speed of light inside a material, or a number off a refractometer: each one turns into an index, a speed and a short list of materials it could be. A beam that meets a glass block at 45° and bends to 27.5° gives n = 1.5318, and the result says plainly that crown glass, rock salt and quartz all fit that reading.

1.544

shared by rock salt and quartz, so the number alone cannot separate them

1.49 to 1.57

where a half-degree slip can move a 45° and 27.5° reading

1.81

about the top of a standard gem refractometer scale, well below diamond

75.0 %

of its vacuum speed is what light keeps inside water

Filling in the form for each method

What do you have? - two angles from an experiment, a speed of light inside the material, or an index someone already measured.
Two angles - the index of the medium the light starts in (air is 1.0003, water 1.333), then the angle of incidence and the angle of refraction, both measured from the normal and both between 0° and 90°.
A speed - the value and its unit, km/s, mi/s or m/s. It cannot exceed 299,792.458 km/s, the speed in a vacuum.
A reading - the index itself, anywhere from 1 up to 5.
Read the result - the index, the speed of light in the material, the critical angle into air, the share of light reflected head-on, and every reference material that fits, highlighted in the table.

What the result is built from

The refractive index is the ratio of the speed of light in a vacuum to its speed in the material, n = c / v. The vacuum speed is exact by definition, 299,792.458 km/s, so a speed of 224,901 km/s gives 1.3330, the index of water. Light inside water keeps 75.0 % of its vacuum speed.

The angle method is Snell's law turned around: n₂ = n₁ × sin θ₁ / sin θ₂. What makes it useful rather than decorative is the second line of the result. A hand-held protractor is rarely better than half a degree, so the calculator moves both angles by 0.5° the unfavorable way and shows the range the true index could sit in. Every reference material inside that range is marked as a match, however many there are.

For a typed reading or a speed the window is 1 % either side, because published values for a single material already spread about that much: cubic zirconia is listed from 2.15 to 2.18, sapphire from 1.762 to 1.778. When nothing fits, the nearest material is named with its distance. Light passing from water into an unknown solid at 40° and bending to 25.1° gives 2.0199; nothing in the list sits in its range, and the closest, cubic zirconia, is 6.94 % higher.

Eighteen reference indices near 589 nm

The same list the result uses, sorted by index, at the yellow sodium line of 589 nm. The critical angle is for light leaving the material into air; the last column is the share of light reflected when it arrives from air straight on.

Material	n	Light speed (km/s)	Share of vacuum speed	Critical angle	Reflected head-on
Vacuum	1	299,792	100.0 %	none	0.00 %
Air	1.0003	299,703	100.0 %	none	0.00 %
Ice	1.31	228,849	76.3 %	49.78°	1.80 %
Water	1.333	224,901	75.0 %	48.63°	2.03 %
Ethanol	1.361	220,274	73.5 %	47.31°	2.33 %
Fused silica	1.458	205,619	68.6 %	43.32°	3.47 %
Glycerol	1.473	203,525	67.9 %	42.77°	3.65 %
Acrylic (PMMA)	1.49	201,203	67.1 %	42.17°	3.87 %
Crown glass (N-BK7)	1.5168	197,648	65.9 %	41.26°	4.21 %
Rock salt (NaCl)	1.544	194,166	64.8 %	40.38°	4.57 %
Quartz (ordinary ray)	1.544	194,166	64.8 %	40.38°	4.57 %
Polycarbonate	1.585	189,144	63.1 %	39.13°	5.11 %
Flint glass	1.62	185,057	61.7 %	38.13°	5.59 %
Sapphire	1.77	169,374	56.5 %	34.41°	7.72 %
Dense flint (N-SF11)	1.78472	167,977	56.0 %	34.09°	7.93 %
Cubic zirconia	2.16	138,793	46.3 %	27.59°	13.47 %
Diamond	2.417	124,035	41.4 %	24.45°	17.19 %
Moissanite	2.65	113,129	37.7 %	22.18°	20.42 %

How much a half-degree slip blurs the answer

Five angle readings run through the calculator. The range is what the index could be if either angle was off by 0.5°, and the last column lists the reference materials inside it.

Light starts in	Angles	Index	Range	Materials that fit
Air	60° / 35.2°	1.5028	1.4770 to 1.5293	acrylic, crown glass
Air	45° / 27.5°	1.5318	1.4934 to 1.5715	crown glass, rock salt, quartz
Air	30° / 19.6°	1.4910	1.4333 to 1.5515	six, from fused silica to quartz
Air	40° / 29°	1.3263	1.2921 to 1.3615	ice, water, ethanol
Water	40° / 25.1°	2.0199	1.9623 to 2.0796	none; nearest is cubic zirconia

Steeper light gives a sharper answer. The range is 0.0523 wide at 60°, 0.0781 at 45° and 0.1182 at 30°, which is why a careful measurement starts well away from straight-on.

What a single reading lands on

The identify method counts a material as a match when its index is within 1 % of your reading. Twelve readings run through the calculator show how wide that net is, and where it catches nothing at all.

Your reading	Matched to	Listed index
1.3333	water	1.333
1.40	no match	nearest: ethanol, 1.361 (2.79 % below)
1.45	fused silica	1.458
1.50	acrylic (PMMA)	1.49
1.53	three: crown glass (N-BK7), rock salt (NaCl), quartz (ordinary ray)	1.5168 to 1.544
1.55	rock salt (NaCl) and quartz, which share one index	1.544
1.60	polycarbonate	1.585
1.70	no match	nearest: sapphire, 1.77 (4.12 % above)
1.75	no match	nearest: sapphire, 1.77 (1.14 % above)
2.00	no match	nearest: cubic zirconia, 2.16 (8.00 % above)
2.30	no match	nearest: diamond, 2.417 (5.09 % above)
2.50	no match	nearest: diamond, 2.417 (3.32 % below)

Two rows deserve a second look. A reading of 1.50, the round figure often quoted for glass, lands on acrylic and not on crown glass N-BK7, because 1.5168 is 1.12 % above the reading, just outside the net. A reading of 1.75 misses sapphire, 1.14 % higher, for the same reason, so a result that close is worth measuring again before you rule a material out.

Five facts about the index that catch people out

Salt and quartz look identical to it. Both read 1.544 at 589 nm. Quartz splits light into two rays, and the second one sees about 1.553; salt, a cubic crystal, does not split it at all.

A jeweler's refractometer cannot read a diamond. A standard gem refractometer tops out near 1.81, the index of the contact liquid it needs. Diamond at 2.417, cubic zirconia at 2.15 to 2.18 and moissanite around 2.65 all read over the limit, so other tests decide.

A glass can out-bend a gemstone. Dense flint N-SF11 has an index of 1.78472, higher than sapphire at 1.77.

Diamond holds light back hard. Inside it light keeps 41.4 % of its vacuum speed, about 124,035 km/s.

Part of the index shows up as shine. Light arriving straight on from air is 2.03 % reflected by water and 17.19 % by diamond.

Who reaches for an index number

A physics lab with a laser pointer and a protractor. The range line says whether the measurement is good enough to name the block, or only good enough to say it is some kind of glass.

Anyone telling clear plastic from glass. Acrylic at 1.49 and crown glass at 1.5168 are 1.8 % apart: too close for a protractor, clear for a refractometer. A reading of 1.50 matches acrylic only, 1.52 crown glass only.

Someone checking a stone against lab data. A report giving 2.415 matches diamond; 2.18 matches cubic zirconia, 0.93 % above the listed 2.16.

Homework with a speed in it. Light moving at 124,000 mi/s gives 1.5023, which fits acrylic and crown glass.

Short answers about measuring n

What is the refractive index of ordinary glass?

Crown glass, the common optical kind, is 1.5168 for N-BK7; flint glass is about 1.62 and dense flint N-SF11 1.78472. A reading of 1.52 matches crown glass and nothing else in the list.

Can the index tell a diamond from cubic zirconia?

By the numbers, easily: 2.417 against 2.16, about 11.9 % apart, far outside the 1 % window. The catch is getting the reading, since both are above what a standard gem refractometer can measure.

Why is an index below 1 refused?

For visible light in ordinary materials n = c / v, and nothing outruns light in a vacuum, so the index is at least 1. X-rays are the exception, seeing indices a hair below 1, but this tool covers visible light. Angles that produce less than 1 are almost always typed the wrong way round: 20° and 40° give 0.5322.

Which angle goes in which box?

Both are measured from the normal, the line perpendicular to the surface, not from the surface itself. Light entering a denser material bends toward the normal, so the angle of refraction is the smaller of the two.

What if my reading matches two materials?

Then the index cannot choose between them and the result says so. A reading of 1.775 fits both sapphire and dense flint, which are only 0.83 % apart; 1.544 fits rock salt and quartz exactly. Hardness, density or how the material splits light settles it.

Do color and temperature change the index?

Slightly. Blue light sees a higher index than red, which is how a prism spreads white light, and most liquids read a little lower as they warm. The reference values are for the sodium line at 589 nm near room temperature.

Can I find a liquid's index without a refractometer?

Roughly, yes. Look straight down at a coin under the liquid and note how deep it appears. For near-vertical viewing, real depth divided by apparent depth approximates the index: water 20 cm deep that makes the coin look 15 cm down gives 1.3333, which the identify method matches to water at 1.333.

How precise does a light speed need to be?

About as precise as the index you want, since n = c / v moves by nearly the same share as the speed. 200,000 km/s gives 1.4990, matched to acrylic; 198,000 km/s, only 1 % slower, gives 1.5141 and crown glass N-BK7 instead.

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