INCLUDING TOTAL INTERNAL REFLECTION AND

THE CRITICAL ANGLE

Light: Reflection & Refraction

Law of Reflection

The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.

Diffuse Reflection

Reflection off of rough surfaces such as clothing, paper, and the asphalt roadway leads to a type of reflection known as diffuse reflection.

Why does a dry road diffuse light, when a wet road specularly reflects.

Index of Refraction

n = c/v The larger the index,

the slower the speed of light

Index of Refraction

Substance Index of Substance Index ofRefraction Refraction

Diamond 2.419 Ethyl Alcohol 1.361Cubic Zirconia 2.21 Ice 1.309

Glass (flint) 1.66 Water 1.333Glass (crown) 1.52 Air 1

Reflection and Refraction at an Interface

Refraction: The Bending of Wavefronts

Index of refraction

Refraction Rules

Light twists inward when entering mediumof higher index of refraction

Refraction Rules

Light twists outward when entering mediumof lower index of refraction

Understanding Refraction

Wheels on axle rolls along a smooth sidewalk and onto grass. Which picturepath is followed? What happens if the motion is reversed?

Understanding Refraction

One side of wave front slows down,and the entire train of fronts twists.

Illustrating Cart Analogy

Right front wheel slows down before left front

Left front wheel slows down before right front

Snell’s (Sahl’s) Law (a history)

Ibn Sahl was an Arabian Mathematician and optics engineer associated with the court of Baghdad. In 984 he wrote a treatise On Burning Mirrors and Lenses in which he set out his understanding of how curved mirrors and lenses bend and focus light. Ibn Sahl is credited with discovering the law of refraction, usually called Snell's law.

In 1621, Willebrord Snellius (Snel) derived a mathematically equivalent form, that remained unpublished during his lifetime.

Snell’s Law

Snell discovered that the ratio between the sine of the incident and refracted angles is equal to the ratio of the incident and refracted velocities.

Snell’s Law continued

Because the velocity of light is extremely difficult to measure, it is more practical to use the indices of refraction. Due to the fact that the velocity is inversely proportional to the index of refraction, you get…

Or…

Law of Refraction: Snell's Law

Right front wheel slows down first.

Snell's Law: n2 sin Q2 = n1 sin Q1

Snell's Law Example

n1 = 1.0 (air) n2 = 1.52 (glass)Q1 = 30 degrees------------------------ n2 sin Q2 = n1 sin Q1

1.52 sin Q2 = 1.0 sin 30 sin Q2 = 0.33

Put calculator inMode Degree

Q2 = sin-1 (0.33) = 19.3 degrees

Rear View Mirror

Rear View Mirror Explained

Apparent Depth in Water

Light exits into medium (air)of lower indexof refraction,and turns left.

More Apparent Depth

Spear-fishing is made moredifficult by the bending oflight.

To spear the fish in the figure,one must aim at a spot in frontof the fish

Refraction at Sunset

Why does the sun appear to beflattened at sunset?---------------------------------------------------The sun actually falls below below thehorizon, i.e., it "sets", a few secondsbefore we see it set.

A Fish-Eye's View

Water on Road Mirage

There's no water on the road; why does it appear so?

The Oasis Mirage

Displacement through a Slab of Glass

Entering and exiting rays are displaced from each other, but parallel.

Internal Reflection

All rays reflect internally, butthe top three rays reflect onlya small percentage internally;most energy leaves the prism. The fourth and fifth rays arereflected 100 % internally.

Internal Reflection

Critical angle…

An incident angle at which the refracted angle is 90o

Note: This can only happen in a case when

light travels from a higher index of

refraction to one with a lower index of

refraction.

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Critical Angle Calculation

What must be Q1 to get Q2 = 90 deg ?

Snell's Law:

n1 sin Q1 = n2 sin Q2

= n2 sin 90 sin Q1 = n2 / n1

------------------------------Assume water to air: n1 = 1.33 n2 = 1.00q1 = sin-1 (0.752) = 48.8 degrees

Qc = critical angle = 48.8 degrees

Cone of Light

Crictical angle for water = 48.8 degrees

Light within the 48.8 degree coneis detected by fish, while nothing in theair outside that cone can be seen.

The only light reaching the fish outsidethe cone is that light (not shown) whichis reflected off the bottom of the pool.

Critical Angle of Diamond

n = 2.419

Qc = sin-1(1.00/2.419) = 24.42 degrees

90.00 - 24.42 = 65.58 degrees

Light outside of 65.58 degreecone is reflected back inside.

Virtually all light entering thetop face of the diamond isreflected internally.

Total internal reflection

When incident light is at an angle greater than the critical angle, the light will reflect instead of refract.

When there is total internal reflection, the light will obey the law of reflection.

Optical Fiber

Optical Fiber

Optical Fibers in Medicine

Broncho Scope Arthroscopic Surgery Colonoscope

Index of Refraction vs Color

v = c/n

The speed of blue light isless than the speed ofred light.

Blue light bends morethan red light.

The Spectrum of White Light

Note that the shorter wavelengths of light are bent more than the longer; blue more than red.

Refraction in a Raindrop

Forming a Rainbow

Rainbow

Index Matching