Images Due to Refraction

You can see an image of things that are in the air.These images are formed by refraction, and they

are different than seeing the actual object.

Where does the fish appear to be?

Do not draw yet.

A B C ?A has the smallest angle.B is an unchanged ray.C has the greatest angle.

Do not draw yet.

A B C ?Water is more dense than air.

Air

Water

density

DENSITY

Do not draw yet.

A B C ?Water is more dense than air.

The index of refraction of water is greater than the index of refratcion of air.

Air

Water

density

DENSITY

n

N

Do not draw yet.

A B C ?Water is more dense than air.

The index of refraction of water is greater than the index of refratcion of air.

The angle in air is greater than the angle in the water.

Air

Water

density

DENSITY

n

Nqq

Do not draw yet.

C The angle in air is greater than the angle in the water.

Draw with a ruler

C ?

No matter where you put your eye, you can see the image of the fish, but where?

eye

eye eyeeye

eyeeye

Draw

No matter where you put your eye, you can see the image of the fish, but where?

All observers agree on the location of the image of the fish. This image is made by

refraction. Draw

The distance from the boundary to the Object (DO) is greater than the distance from the Image to the boundary (DI).

DO

DI

Where does the fly appear to be located?

Air

Water

Air

Water

This ray is coming from the fly.

Air

Water

What is the angle of the ray?

Air

Water

What is the angle of the ray?

Air

Water

q = ?

q

Exactly how do you use this to measure the angle?

Air

Water

q = ?

Air

Water

q = 10˚

Air

Water

The ray continues into the water.What will be its new direction?

Air

Water

The ray continues into the water.What will be its new direction?

Air

Water

Will the angle in the water be lessthan 10˚ or more than 10˚?

Air

Water

Will the angle in the water be lessthan 10˚ or more than 10˚?

density

DENSITY

Air

Water

Will the angle in the water be lessthan 10˚ or more than 10˚?

density

DENSITY

N = 1.00

N=1.33

Air

Water

The angle in the water will be less than 10˚.

density

DENSITYqq

N = 1.00

N=1.33

Air

Water

The angle in the water will be less than 10˚.

n1q1 = n2q2

(1.00)(10˚) = (1.33)(q2)q2 = ?˚

n1sinq1 = n2sinq2

1.00sin10˚ = 1.33sinq2

( 1.00 / 1.33 )sin10˚ = sinq2

q2=InvSin[(1.00÷1.33)sin10˚]q2 = ?˚

How many degrees is the new angle?

n1q1 = n2q2

(1.00)(10˚) = (1.33)(q2)q2 = 7.5˚

n1sinq1 = n2sinq2

1.00sin10˚ = 1.33sinq2

( 1.00 / 1.33 )sin10˚ = sinq2

q2=InvSin[(1.00÷1.33)sin10˚]q2 = 7.5˚

Air

Water

Where does an underwater observer think that the fly is located?

10˚

7.5˚

This is a difficult step.

Please check in on your buddy.

Air

Water

Where does an underwater observer think that the fly is located?

10˚

7.5˚

Air

Water

The fish sees an image due to refraction. The light seems to come from somewhere along the red dashed line.But where?

Please check your buddyon this difficult step.

Air

Water

We’ll need another ray that comes from the fly.Then we’ll see where is the single location from which all of the fly’s rays seem to originate.

Air

Water

Let’s consider this ray.

Air

Water

?

nq = nq(1.00)(0˚) = (1.33)(q)

q = 0˚

nsinq = nsinq1.00sin(0˚) = 1.33sinq

0 = 1.33sinqq = 0˚

Air

Water

Air

Water

Any observer in the water will agree on where the image is located.

Air

Water

These fish agree.Please check your buddy

on this difficult step.

Air

Water

The image is above

the object.

All of the fish see the image of the fly at the same point.

Air

Water

Quantitatively now, where is the image?

Air

Water

What are the values of the: Object Distance andthe Image Distance?

DO=?DI=?

Please measure the Object Distance and the Image Distance.We’ll throw out the highs and the lows.

Air

Water

Object DistanceImage Distance

DO = 10 cmDI = 13 cm

Hmm, what do we know?

DO = 10 cmDI = 13 cm

n = 1.00n = 1.33

Can you figure out what the equation is?

DI = DO (n1/n2)

We’ll need to draw each situation so we know which is greater (DO or DI ),

and then insert the n1 and n2 so that it works out.

(We’ll practice this.)