Basic practice problems

1.  Light hits a piece of plastic at an angle of 50 degrees (with respect to normal).  If the angle of refraction inside is 25 degrees, what is the index of refraction of this plastic?  Also, what is the speed of light inside the plastic.

2.  What is the frequency of light with a wavelength of 100 nm in air (where it travels pretty much at the speed of light).  (That's 100 x 10^-9 m.)

3.  A lens has a focal length of -25 cm.  A candle is 10 cm in front of it.  Find the following:

a.  type of lens
b.  location of image (di)
c.  type of image
d.  magnification of image
e.  whether image is up or down
f.  whether image is real or virtual

Answers

1. 

1.8

1.66 x 10^8 m/s

2. 3 x 10^15 Hz

  

3.  concave, -7.1 cm = di (making it virtual), mag = -0.7  (which makes it smaller and upside-down)

Answers from recently turned in homework

1.

a.  convex (since the f is +)
b.  di = 60 cm.  Use the lens equation:  1/f = 1/di + 1/do
c.  magnification = -2.  Use the magnification equation:  mag = -di/do
d.  real (since di is +)
e.  upside-down, since the mag is -

2.  Dimmer, but still in focus.  Fewer light rays make it, but their path is not changed.

3.  Place the object AT the focal length.

4.  Either within f, or between f and 2f

Test review stuff.

Review for test:

Law of reflection – angle in = angle out

Refraction:  what is it, why it is

Index of refraction:  n = c/v

Snell’s law:  n1 sin(theta 1) = n2 sin(theta 2)

Other equations:  v = f l

Also worth remembering:  f does NOT change during refraction, but v and l will

Remember:  normal line (perpendicular to surface of optic)

Lenses and mirrors:  convex lens and concave mirror (both have +f); concave lens and convex mirror (-f)

Lens equation:  1/f = 1/di + 1/do

Magnification:  mag = -di/do.  Also, hi/ho (height of image divided by height of object)

-mag = upside-down image; +mag = right-side up image

Absolute value of mag tells you whether image is larger ([mag] > 1) or smaller than object ([mag] < 1)

Real (+di) vs. virtual image (-di)

Critical angle and total internal reflection:  sin(critical angle) = 1/n

Questions to expect:

1.       Snell’s law (like quiz)

2.       Lens (like HW)

3.       Miscellaneous:  you’ll choose 1 or 3 (or so) 

a.       Essay covering some abstract situation or problem

b.      More mathematical/theoretical question

c.       Demonstration?

d.      Practical (where you have to DO something or look at something)

e.      ??? (mwa ha ha ha ha…..maniacal laugh)

HW to TURN IN next class

Consider a lens with a focal length of +20 cm.  An object is 30 cm in front of it.

1.  Determine the following:

- type of lens
- location of image
- magnification of image
- type of image (real or virtual)
- whether image is right-side up or upside down

2.  What would be the effect of covering up half of the lens?

3.  Where could you place the object such that you get NO image?

4.  Where could you place the object such that you get a larger image?

HW - start thinking about the lab report

In the next 2 weeks, we'll have a quiz (or graded homework), test and formal lab.  The goal is to finish optics before winter break - there is enough time for this, without rushing.

Start thinking about (and writing) the formal lab.  Here is what you will need:



Basic structure of the lab report:

* Title

* Purpose of lab

* Data table - include all columns from your data, AND 1 more column:  calculated f

* Find the average f, and the percent error between your average and the expected f from the lens.

* Sample calculation for focal length (your data table will have ALL of the calculated values, but there is only need for one calculation to be shown)

* Graph(s) if you made any (they are not required, but a graph of di versus do might be instructive)

* Conclusion - probably the biggest, most detailed part of the lab.  Include the following:

 - Give sources of error.

 - Discuss how the image formation depends on object distance.  Note if there "transition points", etc.  This is the tough part of the conclusion (and the most mathematical).

- Discuss a technique for measuring the focal length of a concave lens (or convex mirror).

- Discuss the similarities between convex and concave mirrors and lenses.

 - Give a general conclusion.

HW

Think about the things from today.  Also:

Under what circumstances do images form at the focal point of a lens, if ever?

What is a virtual image?

Can a focal point/length be negative?  What would that mean?

HW

Hi there!

Have a look through your lab data to see if there is anything interesting.

Also, look up the term "focal point" (or "focal length").  How is this related?

Thanks!

>

Sorry for delay - this was posted to the wrong blog.

Due Monday in class at beginning

HW light problem

HW

For next class, come with a definition of:

Total internal reflection and/or critical angle

Also, why do you think prisms break up light?

HW

Make sure your calculator is in degrees mode.  To check, hit the MODE button and look for the row (3rd down?) which reads "radian degree".  If "degrees" is not highlighted, scroll down to it and hit ENTER.  Then close MODE by hitting 2ND MODE.

1.  What is the index of refraction for a substance that slows light down to half its speed in a vacuum?

(2)

2.  What is the index of refraction for a substance that takes an initial light ray in air at 50 degrees (WRT to a normal line) and bends it to 34 degrees?

(1.37)

3.  A light ray hits a block of plexiglass (n = 1.65) at 45 degrees.  What is the angle of refraction inside the block?

(25.5 degrees)

Trig Practice, if you need it.

Consider a 5-12-13 right triangle.

1.  Draw this.  Let the 5 side be horizontal (adjacent side).  13 is obviously the hypotenuse and 12 is the opposite side.

2.  So that we are on the same page, consider your reference angle as the angle between 5 and 13.

3.  Find the values for sin, cos and tan of the reference angle.

(12/13, 5/13, 12/5)

4.  Use the 2ND SIN function to find the angle itself.  (You could also use 2ND COS or 2ND TAN.)

2ND SIN (12/13) = 67.38 degrees

5.  Repeat this for an 8-15-17 triangle, if you have time.

FYI:  https://en.wikipedia.org/wiki/Pythagorean_triple



Part 2.  Calculator practice.  Find these:

1.  sin 0

(0)

2.  sin 30

(0.5)

3.  sin 45

(0.707)

4.  sin 60

(0.866)

5.  sin 90

(1)

6.  cos 0

(1)

7.  cos 45

(0.707)

8.  cos 60

(0.5)

9.  cos 90

(0)

Inverse practice.  Find the angle, knowing that:

1.  sin (theta) = 0.6

(36.9 degrees)

2.  sin (theta) = 0.25

(14.5 degrees)

3.  cos (theta) = 0.75

(41.4 degrees)

(If you've forgotten how to do these, recall the part about the 2ND SIN (or 2ND COS) functions.)

Probably the most important thing to remember here is what sine, cosine, and tangent actually represent -  they are RATIOS of sides associated with a particular angle.  For example, if a right triangle has a 30-degree angle in it, the sine of that angle (0.5) tells us that the ratio of the length of the side opposite that angle to the length of the hypotenuse is 0.5.

On the other hand, if we only knew the sine value (or cosine or tangent value), we could use that information to find the angle itself.  In the old days, you'd look up a value in a big chart.  Now, your calculator goes through an algorithm to solve for the angle.

HW

For HW

Come to class with definitions of:

index of refraction

Snell's law

Also:

https://www.youtube.com/watch?v=EtsXgODHMWk

HW for Monday

Comc to class with definitions of:

Reflection
Refraction
Dispersion
Diffraction

The answers should have something to do with light.

This is posted on Friday, so I'll understand if you don't get to it.

Happy weekend!

Quick organ pipe/tube problem

What is the resonant frequency of a tube that is 0.4-m long?  Assume that the speed of sound is 340 m/s.

What are the frequencies of the next 2 harmonics in this tube?

Doppler effect

Doppler effect!

http://www.lon-capa.org/~mmp/applist/doppler/d.htm

The key in the Doppler effect is that motion makes the "detected" or "measured" frequencies higher or lower.

If the source is moving toward you, you detect/measure a higher frequency - this is called a BLUE SHIFT.

If the source is moving away from you, you detect/measure a lower frequency - this is called a RED SHIFT. Distant galaxies in the universe are moving away from us, as determined by their red shifts. This indicates that the universe is indeed expanding (first shown by E. Hubble). The 2011 Nobel Prize in Physics went to local physicist Adam Riess (and 2 others) for the discovery of the accelerating expansion of the universe. Awesome stuff!

http://www.nobelprize.org/nobel_prizes/physics/laureates/2011/

It's worth noting that the effect also works in reverse. If you (the detector) move toward a sound-emitter, you'll detect a higher frequency. If you move away from a detector move away from a sound-emitter, you'll detect a lower frequency.

Mind you, these Doppler effects only happen WHILE there is relative motion between source and detector (you).

And they also work for light. In fact, the terms red shift and blue shift refer mainly to light (or other electromagnetic) phenomena.

Sites from class today AND HW (for next Tuesday)

Some of these are repeats from the other day:

Anna-Maria

https://www.youtube.com/watch?v=vC9Qh709gas

https://www.youtube.com/watch?v=UHTF1-IhuC0&feature=iv&src_vid=vC9Qh709gas&annotation_id=annotation_1970696487

https://www.youtube.com/watch?v=WlDi2XpK_dQ


Shattering wineglass

https://www.youtube.com/watch?v=cPALfz-6pnQ


Ruben's tube (from me)

https://www.youtube.com/watch?v=cqilJNsiqig


Longitudinal vs. transverse waves

http://www.animatedscience.co.uk/blog/wp-content/uploads/focus_waves/tl-wave.html

Animated:

http://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html

http://www.acs.psu.edu/drussell/Demos/rad2/mdq.html


Wave forms in tubes

http://www.acs.psu.edu/drussell/Demos/StandingWaves/StandingWaves.html


>

Practice problems:

Consider the musical note G, 392 Hz.  Find the following:

1.  The frequencies of the next two G's, one and two octaves above.

2.  The frequency of the G one octave lower than 392 Hz.

3.  The frequency of G#, one semi-tone (piano key or guitar fret) above this G.

4.  The frequency of A#, 3 semi-tones above G.

5.  The wavelength of the 392 Hz sound wave, assuming that the speed of sound is 340 m/s.

6.  What are the differences between longitudinal and transverse waves?  Gives examples of each.  What type of wave is sound?

7.  Use graphsketch.com/ and try to graph some functions.  Set the x-range as -6.3 to +6.3, and the y-range from -4 to +4.  Then graph these:

y = 3 sin(x)
y = sin(2x)
y = sin(x) + cos(x)
y = 2 sin(x) - 3cos(x)

Play around with anything that looks fun.  No need to write anything or print anything out - just play around with graphsketch.  If you're feeling ambitious, have a look at desmos.com.

PS.  I chose the x-range as I did because graphsketch uses radians (not degrees).  6.3 is close to 2pi, and 2pi is equal to 360 degrees.

Plan on a test next Thursday.  Yay!

HW due Friday (10/23)

Part 1

Review the concepts of how we make musical scales, in light of the equal-tempered scale.  Worth a look, if you have time:

https://en.wikipedia.org/wiki/Equal_temperament

Of particular note (heh, get it?):

Twelve tone equal temperament took hold for a variety of reasons. It conveniently fit the existing keyboard design, and permitted total harmonic freedom at the expense of just a little impurity in every interval. This allowed greater expression through enharmonic modulation, which became extremely important in the 18th century in music of such composers as Francesco Geminiani, Wilhelm Friedemann Bach, Carl Philipp Emmanuel Bach andJohann Gottfried Müthel.

With what we learned in class in mind, find the frequencies of:

A (one octave above concert A)
A (two octaves above concert A)
A (one octave below concert A)
A# (one semi-tone above concert A)
B (two semi-tones above concert A)

Recall that concert A is 440 Hz, and our multiplier (the 12th root of 2) is 1.059.

Part 2

Come to class with definitions of longitudinal and transverse waves.  Also, review these pages;


http://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html

http://www.animatedscience.co.uk/blog/wp-content/uploads/focus_waves/tl-wave.html

http://www.acs.psu.edu/drussell/Demos/rad2/mdq.html


FYI, the device I used in class today was called a Ruben's tube.

Wave-age.

Wave practice!

Work out in your notes.  These will be reviewed on Friday.

Recall also:

v = f l

c = 3 x 10⁸ m/s (speed of light, including any type of electromagnetic wave)

1.  What is the wavelength of the radio station 97.9 ("98 Rock").  Keep in mind that the number refers to the frequency in MHz, and note that MHz means 'million (x 10⁶) Hz."

2.  The visible range of human eyesight is 700 nm to 400 nm.  What are the frequencies associated with this, and which end is red and which is violet?

3.  Find the speed of a 500 Hz wave with a wavelength of 0.4 m.

4.  What is the frequency of a wave that travels at 24 m/s, if 3 full waves fit in a 12-m space?  (Hint:  find the wavelength first.)

5.  Approximately how much greater is the speed of light than the speed of sound?

6.  Harmonics

a.  Draw the first 3 harmonics for a wave on a string.

b.  If the length of the string is 0.5-m, find the wavelengths of these harmonics.

c.  If the frequency of the first harmonic (n = 1) is 15 Hz, find the frequencies of the next 2 harmonics.

d.  Find the speeds of the 3 harmonics.  

7.  (Review) Differentiate between mechanical and electromagnetic waves.  Give examples.

9.  (Review) Draw a wave and identify the primary parts (wavelength, crest, trough, amplitude).

10.  The note C vibrates at 262 Hz (approximately).  Find the frequencies of the next two C’s (1 and 2 octaves above this), and the frequency of the C below it.

11.  A red LED has a wavelength of 662 nm.  What is the frequency of light emitted from it?  (nm refers to x 10^-9 m)

Also...

DRAFT for this lab is due Thursday, 10/15.  Final lab will be due the class after that (Monday).

Ok?  OK!

Lab handout FYI

Harmonics on a string

A special area of wave physics involves "harmonics on a string."  Harmonics arise due to reflected waves interfering with incoming waves.  At the right frequencies, resonance occurs - so, the "standing wave" can get a pretty big amplitude with minimal energy input.  This phenomenon is a lot like pumping the swings to make yourself go higher.  In general, a string has a lowest possible frequency (the "resonant frequency") at which it will vibrate naturally - imagine plucking a string and hearing the note that results.  However, there are other frequencies ("harmonics") that can be produced that will also cause familiar wave patterns.  That's what today's lab is all about.

In this lab, you will determine the relationships relevant for harmonics on a string.  First, some definitions:

harmonic number, n

- this is the number of "humps" or "half-waves" present on a string.  The sequence starts at 1 and goes up higher and higher (by integers) until the string doesn't exhibit much wave motion to the naked eye (though indeed there may still be harmonics)

wavelength, lambda (l)

- literally, the size of a complete wave.  Crest-to-crest or trough-to-trough distance.  Could also be the distance between any 2 points in phase with each other

frequency, f

- the number of waves or vibrations or oscillations per second

wave speed, v

- the rate at which the wave energy travels.  Could conceivably be measured with a stopwatch, but is better computed with the equation:  v = f l

Procedure

Set up a wave oscillator apparatus, with a pulley attached to a table.  Your string will be draped over the pulley.  Make sure the string is firmly attached to the oscillator and a weight is attached to the end of the string.

Measure the effective length of the string:  from oscillator to top of pulley.  Also measure the hanging mass.

Part I

1.  Starting very low, find the lowest possible frequency (on the sine wave generator) that gives you an n=1 (lowest) harmonic -- this is ONE hump.  Record frequency.

2.  Gradually increase the frequency, advancing through a series of harmonics.  Record n and f.  Do as many harmonics as you can. 

3.  In a table, record n, f, l and v.  You will need to calculate l and v.

Determine trends worth noting.

Part II

Chat with other groups – those who used a different hanging mass.  See if you can determine if there are differences due to the weight that hangs (and provides tension in the string).

Questions

1.  What seems to be clear from your data in part I?

2.  What seems to be clear from your data in part II?

3.  You may not play a stringed instrument, but what can you infer from your experiment as it relates to guitars, violins, etc.?

4.  Write a general conclusion – things you learned, things that were interesting, sources of error (threats to validity), suggestions for improving the experiment, and so forth.

Your complete lab report should include:  a title, date(s) performed, lab partner(s), purpose of lab (at the beginning), data, graphs (if relevant), pictures (if helpful), sample calculation (though all calculations will be done), conclusion and answers to questions.

Lab guidelines

Calculations:

Wavelength:  2L/n

Determine the speed of the wave for each trial, using the expression:  speed = frequency x wavelength.  The speed values should be in the data table.

The data table should have:  harmonic number (n), frequency, wavelength, speed.  Mass and length must be somewhere as well (or in the table).

In your conclusion, discuss the mathematical relationships you've found.  For example, how are frequency and harmonic number related?  How does tension affect the frequency?  For that question, you'll need to chat with other lab groups.

Also include sources of error for this experiment.

Basic structure of the lab report:

Title

Purpose of lab

Data table

Sample calculation for speed (your data table will have ALL of the calculated values, but there is only need for one calculation to be shown)

Graph(s), where relevant

Conclusion - probably the biggest, most detailed part of the lab.  This will have answers to lab questions (unless you wish to have a separate section for those), sources of error, ways to improve the experiment, anything interesting you learned, problems you faced in the lab, etc.

HW

Come to class with a definition of "standing waves" and "harmonics".

Intro to waves

So - Waves.....  

We spoke about energy.  Energy can, as it turns out, travel in waves.  In fact, you can think of a wave as a traveling disturbance, capable of carrying energy.

There are several wave characteristics (applicable to most conventional waves) that are useful to know:

amplitude - the "height" of the wave, from equilibrium (or direction axis of travel) to maximum position above or below

crest - peak (or highest point) of a wave

trough - valley (or lowest point) of a wave

wavelength (l) - the length of a complete wave, measured from crest to crest or trough to trough (or distance between any two points that are in phase - see picture 2 above).  Measured in meters (or any units of length).

frequency (f) - literally, the number of complete waves per second.  The unit is the cycle per second, usually called:  hertz (Hz)

wave speed (v) -  the rate at which the wave travels.  Same as regular speed/velocity, and measured in units of m/s (or any unit of velocity).  It can be calculated using a simple expression:

There are 2 primary categories of waves:

Mechanical – these require a medium (e.g., sound, guitar strings, water, etc.)

Electromagnetic – these do NOT require a medium and, in fact, travel fastest where is there is nothing in the way (a vacuum). All e/m waves travel at the same speed in a vacuum (c, the speed of light):

c = 3 x 10^8 m/s

First, the electromagnetic (e/m) waves:

General breakdown of e/m waves from low frequency (and long wavelength) to high frequency (and short wavelength):

Radio

Microwave

IR (infrared)

Visible (ROYGBV)

UV (ultraviolet)

X-rays

Gamma rays

In detail, particularly the last image:

http://hyperphysics.phy-astr.gsu.edu/hbase/ems1.html

http://csep10.phys.utk.edu/astr162/lect/light/spectrum.html

http://www.unihedron.com/projects/spectrum/downloads/full_spectrum.jpg

Mechanical waves include:  sound, water, earthquakes, strings (guitar, piano, etc.)....

Again, don't forget that the primary wave variables are related by the expression:

v = f l

speed = frequency x wavelength

For e/m waves, the speed is the speed of light, so the expression becomes:

c = f l

Note that for a given medium (constant speed), as the frequency increases, the wavelength decreases.