Refraction Equations | Show Me The Physics

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Which media is faster, Y or Lucite?

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Explain This

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The Physics of the Human Eye

image of Eye on retina

Graphic from dorling kindersley books website

Video Instruction

showmethephysics.com

Fill In the Blank Notes

D. Index of Refraction (n) – a comparison of speed of light in a substance to its speed in a vacuum

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If a substance has an index of refraction of 2.00 it means light is twice as fast in a vacuum than it is in that medium

n = c/v

c = speed of light in a vacuum
(3.00 x 10⁸ m/s)

v = speed of light in a medium

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n_vacuum = 1.00

n_air ≈ 1.00 , v ≈ 3 x 10⁸ m/s

Which substance slows down light the most when light enters from air?

Diamond,

(highest (n) index of refraction)

least?

Water

(smallest (n) index of refraction)

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Any device with a lens refracts light

Ex 1) Speed of light in alcohol?

n = 1.36 (Reference Table)

n = 1.36 = c/v

1.36 = (3.00 x 10⁸ m/s)/V

3.00 x 10⁸ m/s = 1.36V

V = 2.21 x 10⁸ m/s

Magnifying glasses enlarge objects with refraction

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http://www.freeimages.co.uk/

n & v relationship?

n = c/v

Inverse

The more light is
slowed down

or sped up,

the more
it changes direction

Refraction in Glass

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The human eye refracts light

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1. Prediction θ_ref from θ_in

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a. Snell's Law

n₁sinθ₁ = n₂sinθ₂

1 – incident medium

2 – refractive medium

Air/Lucite

n₁sinθ₁ = n₂sinθ₂

1.00 sin53 = (1.50) sinθ₂

.798 = 1.50sinθ₂

.798/1.50 = sinθ₂

.532 = sinθ₂

(inverse sine .532)

θ₂ = 32⁰

Ex) Light refracts as it moves from water to flint glass. Which angle is bigger, q_in or q_ref?

Faster medium has bigger angle

Water 1.33?? or Flint glass 1.66??

Angle of Incidence bigger, Water faster

Ranking $Refraction Equations lesson illustration$ Task

Rank the media below from
fastest to slowest

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Fooling Drinkers With Refraction

More Refraction Equation
Instruction

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Enrichment

NOVA (PBS) explains how refraction makes diamonds sparkle

Check Your Understanding

5 quick questions — pick an answer to see if you’re right.

1. A substance has an index of refraction of 2.00. What does this mean?

2. A material has an index of refraction of 1.50. What is the speed of light in it?

3. Light in air (n = 1.00) strikes glass (n = 1.50) at 30° from the normal. What is the angle of refraction? (sin 30° = 0.50)

4. How are a material's index of refraction (n) and the speed of light in it (v) related?

5. Light passes from water (n = 1.33) into flint glass (n = 1.66). Which angle is larger?

NYSSLS Regents Practice · Waves · Snell’s Law

A Laser Into an Aquarium

A laser beam in air strikes the flat water surface of an aquarium with an angle of incidence of 30.°. The index of refraction of water is 1.33.

What is the angle of refraction in the water?

▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)

Challenge score: 0 / 6

Support or Refute · Justify

C1. A student makes the following claim.

Claim: If the laser’s angle of incidence is doubled from 30.° to 60.°, the angle of refraction in the water also doubles, to about 44°.

Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.

Support Refute

Multiple choice

C2. The laser beam continues from the water into the glass bottom of the tank (n = 1.52). How does it bend?

Substitute values

C3. The laser is tilted so that its angle of incidence on the water is 50.°. Substitute numerical values into a mathematical representation that can be used to determine the angle of refraction in the water. Then calculate the angle.

() sin (°) = () sin θ₂, so θ₂ = °

Determine the value

C4. For the original 30.° beam, the refracted ray (at about 22° in the water) continues to the flat glass bottom of the tank (n = 1.52). Determine the angle of refraction in the glass.

θ_glass = °

Multiple choice

C5. A beam goes from water into air at an angle of incidence of 30.°. What is the angle of refraction in air?

Constructed response

C6. A fish swims at the bottom of the aquarium. A spear aimed straight at the fish’s image would miss, but the laser aimed straight at the image hits the fish. Explain why.

Refraction Relationships →