Refraction of Light

Lesson 3

(3 hours)

Refraction of Light

Word bank

REFRACTION

The bending of an oblique ray of light when it passes from one transparent medium to another

Refraction of Light

• When an incident ray passes through different media, from air to glass for example, the resulting ray bendsWhy?Because light changes its speed upon entering a different medium

air

glass

Refraction of Light

• In general, REFRACTION is the change in the direction of a wave as it crosses the boundary between two media in which the wave travels at different speeds

• Light generally slows down upon entering a denser medium, refracting closer to the normal line

Refraction of Light

Word bank• ANGLE OF INCIDENCE

the angle between the incident ray and the normal

• ANGLE OF REFRACTION

the angle between the refracted ray and the normal

Refracted ray

Incident ray

Angle of refraction

Angle of incidence

Normal

CONCEPT CHECK

• Light slows down upon entering a denser medium. How would you compare the angle of incidence and the angle of refraction?

• If light moves instead, from a dense medium to a less dense medium, what will be its behavior? How would you compare the angle of incidence and the angle of refraction?

Refraction of Light

Word bank

INDEX OF REFRACTION (n)

Ratio of the speed of light in free space (c) and the speed of light in a particular medium (v)

Given by the equation:

where c = 3.0 x 108 m/s (constant) Note: Free space would include vacuum (outer space) and air

v

cn

EXAMPLE

Light travels at 3.00 x 108 m/s through air. It slows down to 2.26 x 108 m/s in water. What is the index of refraction of water?

Given:c = 3.00 x 108 m/s (speed of light in free space)

v = 2.26 x 108 m/s (speed of light in water)

n = ?

SOLUTION

n = c/v

= (3.00 x 108 m/s)/(2.26 x 108 m/s)

= 1.33

Index of refraction has no unit since the units of c and v (both m/s) will

cancel out

Refraction of Light

Here are some of the indices of refraction of common materials:

Substance n

AirBenzeneDiamondEthyl AlcoholGlass, CrownGlass, FlintIceLucite & PlexiglasQuartzWater

1.001.502.421.361.521.631.311.511.461.33

HOMEWORK

• Determine the speed of light in each of the materials given in the previous slide.

• What is the relationship between the index of refraction and the speed of light in the given material?

• In what material does light travel the fastest? the slowest?

Refraction of Light

SNELL’S LAW

The ratio of the sines of the angles of incidence and refraction is equal to the ratio of the speeds of light in the two media.The equation was derived by Willebrord Snell

2

1

v

v

sin

sin

r

i • i = angle of incidence• r = angle of refraction• v1 = speed of light in the first medium • v2 = speed of light in the second medium

EXAMPLE

Light travels at 3.00 x 108 m/s through air. It slows down to 2.26 x 108 m/s in water. If it enters the water at an incidence of 30º, what is the angle of refraction?

Given:

Light travels from air to water so air is the 1st medium and water the 2nd medium

v1 = 3.00 x 108 m/s v2 = 2.26 x 108 m/s

i = 30º r = ?

SOLUTION

sin r = (v2sini)/v1

= (2.26x108 m/s)(sin 30º)/(3.00x108 m/s)

= 0.376666666

to solve for r:

r = sin-1 (0.37666666)

= 22.13º

Refraction of Light

The two previous equations can be combined into a restatement of Snell’s Law:

rnin sinsin 21

v

cn

1

2

2

1

v

v

sin

sin

n

n

r

i

can be expressed in terms of speeds of light in the two media,

11 n

cv

22 n

cv and

Plugging in the two equation for v Snell’s law becomes

Alternately, we can write Snell’s law as:

Refraction of Light

rnin sinsin 21 •n1 = index of refraction of the 1st medium•i = angle of incidence •n2 = index of refraction of the 2nd medium•r = angle of refraction

EXAMPLEA beam of light enters a diamond at an angle of incidence of 20º. Determine the angle of refraction of diamond.Given:If the 1st medium is not mentioned, we can always assume that it’s air. Checking the table for the index of refraction of air and diamond, we have

n1 = 1.00 i = 20º

n2 = 2.42 r = ?

SOLUTION

sinr = (n1sini)/n2

= (1.00 sin 20º)/(2.42)

= 0.141330637to solve for r

r = sin-1(0.141330637)

= 8.12º

YOUR TURN

A flashlight is frozen into a block of ice. If its beam strikes the surface of the ice at an angle of incidence of 37°, what is the angle of refraction?

i = 37°

r = ?air

ice

ANSWER: r = 52°

HOMEWORK

1) What is the angle of refraction of a beam of light that enters the surface of a lake at an angle of incidence of 50°?

2) A beam of light strikes a pane of glass at an angle of incidence of 60°. If the angle of refraction is 35°, what is the index of refraction of the glass?

Refraction of Light

REFRACTION IN NATURE

• During a hot day, we see distorted images in the horizon. This warping of images is called ATMOSPHERIC REFRACTION and is caused when light crosses a region of hot air. The distorted image is called a MIRAGE.

Refraction of Light

REFRACTION IN NATURE

• When allowed to pass through a prism, white light splits into its component colors. This process is called DISPERSION. A rainbow is a natural dispersion of light in the sky.