Snell’s Law A way to figure out exactly how

much light will bend!!

Students in grade 10 math – try examples

To be included on Formal Lab• Introduction• Purpose (one for both)• Hypothesis - Not required• Materials (one for both)• Procedures (A & B)• Observations (A & B)• Sample Calculations• Error Analysis - precision of

instrumentation

• Discussion Questions (1-7 & 1-8)

• Diagrams• Conclusion

Diagrams

Review:

• Light travelling from fast to slow bends TOWARDS THE NORMAL

• Light travelling from slow to fast bends AWAY from the NORMAL

• HIGH “n” means material is SLOW

• LOW “n” means material is FAST

Amount of Refraction

• The amount of refraction will depend on– The difference in the speeds of the two materials

• The bigger the difference, the more refraction occurs

– How big the angle of incidence is • the bigger it is, the more refraction will occur

Snell’s Law

sin

sini r

r i

n

n

1 2

2 1

sin

sin

n

n

OR

What is “sin”?• Stands for sine and it is a mathematical term.• It represents the ratio of the length of the side

opposite of a certain angle to the length of the hypotenuse in a right angle ( ) triangle

90

adjacent

• e.g. 300sin = 0.5

300

This means that the side opposite to the angle is half the length of the hypotenuse.

This could mean that possible triangles are

Side A: 0.5 cm, Side B: 1 cmSide A: 1 cm, Side B: 2 cmSide A : 20 cm, Side B: 40 cm

AB

You will learn more about it in grade 10 math, so for now we will mostly learn how to use it for Snell’s Law only…

In order to properly use the sine ratio:• First – make sure your calculator is set on

degrees!!! To get sin 30o, just press sin and then 30 on your calculator!(for some calculators you have to press 30 then sin)

Check the others in the table…

A little harder to remember…

e.g. if you are told that

and asked to find then you have to use the “second function” button and sin-1

sin 0.5

1

0

sin 0.5

sin (0.5)

30

Notation important!

sin

sini r

r i

n

n

medium #1: Slow

medium #2: Fast

normalincident ray

refracted ray

i

r

Rearranged versions that are maybe easier to memorize:

sin sini i r rn n

1 1 2 2sin sinn n or

So long as the order is met, subscripts are completely arbitrary and you can choose any letters that suit the situation in order to make Snell’s Law easier to work with during the question

1. Calculate the index of refraction of cubic zirconium (fake diamond) if the angle of incidence in water is 50.0o and the angle of refraction in the cubic zirconium crystal is 27.0o. (Note: the index of refraction of water is 1.33)

50o

27o

Waternw=1.33

Cubic zirconium

nz=

sin sinw w z zn n

0 01.33sin 50 sin 27zn

0

0

1.33sin 50

sin 27 zn

2.24zn

Index of refraction of zirconium is about 2.24.

Make sense? •nz is bigger than nw

• this means that cubic zironium is slower than water•Refracted ray should bend towards the normal• It does!!! Makes sense!!!

• 2. When light passes from crown glass (n=1.52) into ice

(n=1.31) at an angle of incidence of 300, what is the angle of refraction?

30o

sin sing g i in n

01.52sin 30 1.31sin i

01.52sin 30sin

1.31 i

sin 0.5801...

The angle of refraction would be about 350 (bends away - makes sense)!

•ng is bigger than ni

• light is moving from slow to fast•Should bend away from the normal

i

1sin (0.5801...)

035

Crown glassng=1.52

Iceni=1.31

Common errors:• This is not the same as the x-1 button we used

for the mirror equation.

• If you get an error message, you were probably trying to do sin-1 to a number bigger than 1 which is impossible…(it is impossible because the hypotenuse has to be the longest side and

• You can’t divide by sin…has to have an angle with it!

sinopposite

hypotenuse