Lenses

Lenses

Objective:

 To observe characteristics of a converging lens when the object is placed on one side of the lens and the real, inverted image is placed on the other side of the lens.

Equipment:
socket lamp with V-shaped filament
Large converging lens
masking tape
Lens Holder
piece of cardboard (or other flat surface)
Track for lens
Meter stick

Procedure: 

     The focal length was recorded by taking a source that was "infinitely" far, the sun was used in this experiment because in comparison to the lens it is infinitely far away and arranging it around to find a point where the image was focused. A meter stick was used to find the distance between the lens and the focused image. This was 0.0485 ±0.0030 m.

 The following was set up by placing the lens into the lens holder and creating a track for the lens (using a meter stick and some stands). 

     The length of the arm of the image from the circle to the end of the line was take as the object image (9.2±2.0 cm). We place the image about 1.5 focal lengths away and used the cardboard to focus the resulting image. The image height and distance from the lens was recorded. From this the magnification could be found by dividing the image height by the object height. (If the lens was rotated the image remained the same). The image was always inverted.This was repeated for various multiples of the focal length.

All of these values were measured in cm. The object distance and image height values were plus or minus 0.2cm while the image distance was about plus or minus 1.5cm.

Data Analysis:

 If the object was at a distance that was less then one focal point the object height was too large to distinguish. A graph of image distance vs object distance was made and showed a nonlinear relationship. But when we graphed the inverse of negative object distance vs the inverse of image distance we got a somewhat linear relation within the given error. Do to it being an outlier the fifth data point was removed from the calculation of the plot.

 Video of focusing image.

The y intercept was 0.2208 which represents the inverse of image distance as the object distance reaches infinity. This is the inverse of the focus. The relationship between Inverse object distance (x) and inverse of image distance (y) is given in the equation in the above image.

Mirror lab

Objective:

 Explore the images formed by convex and concave mirrors.

Equipment:

Convex mirror
Concave mirror
An object
Ruler

Procedure:

This lab involved the examination of two types of mirrors, concave and convex.

     convex mirror-

 A marker was placed in front of the convex mirror.The image appears smaller than the actual object but the object is upright. The image seems further from the mirror then the actual object.        With a ruler placed normal to the mirror's center  we held the mirror a distance of 0.50m. The height of the marker (our object) was 0.12m. Measuring the size of the image of the marker gave us 0.067m when the object is moved closer increases in size and when moved further decreases.

  concave mirrors

the object was now placed in front of a convex mirror. The object appeared larger and iverted. When the object moved closer it appears upright, and still magnified. The image also appears closer to the mirror then the actual object. Using the ruler  we again placed it 0.50m from the center and we observed an inverted height of 0.21m.

Analysis:

 This phenomenon can be explained by using a diagram of light rays being reflected off the pen.
 For the convex mirror you see that the point where these rays intersect is where the top of the marker's image appears and this agrees with our observation

Concave Ray Diagram

For the concave mirror we see the focus and center of the sphere is outside of the mirror. Using the rays it can be seen that the object appears to be inverted which also agrees with our observation.

Convex Ray Diagram

From this it can be concluded that the image size and orientation depend on the focus or center of the spherical mirror.

Refraction

Refraction

Objective: 

To find a relationship between the angle that the light enters a medium and the angle at which the light is refracted by traveling through the medium. 

Equipment:

Light Box

Light box or Laser

Semicircular plastic or glass prism

circular protractor (or some way of measuring the incident and refracted angles)

Light box plus protractor

Procedure:

In performing this experiment a light box with a small slit was set up with a beam of light aimed at a semi-circular prism. A paper protractor was used to determine the angle at which the light entered to prism as well as with which angle it exited the prism. This was done by increasing the initial angle, (angle of incidence), by small increments. And recording the resultant exiting angle. Two cases were observed, the first with the incident angle at the flat surface and the second case being with the incident angle at the curved surface. The sines of the data gathered was then graphed to analyze the data.

Case 1

Sintheta1 vs sine theta 2

Case 2 

sintheta 1 vs sintheta 2 

Analysis:

TIR

In both case 1 and 2 it can be observed that the slope of the graph is equal to the ratio of the speed of light in the medium and the speed of light in air. this is also known as the index of refraction. However in case two after surpassing a certain angle total internal reflection is observed, TIR. This happens when the exiting angle, angle of refraction has exceeded 90 degrees, the angle of incidence at which this phenomenon occurs is known as the critical angle.

Speed of Sound 

Objective:

 Verify the speed of sound.

Equipment:

Logger Pro with Microphone

Computer

Long Tube

Meter Stick

Tube plus microphone set-up

Procedure:

A trial

Another trial

To perform this lab the long tube was lain horizontally and the microphone placed at one end of it. A sound was then produced, using logger pro the sound was recorded graphically. The time from the first large peak (beginning of snap) to the first big peak of the second sharp area ( beginning of snap echo) was recorded. This time along with with the recorded length of the tube was used to calculate the speed of sound using distance/time = velocity. This was repeated six times in order to 

find an average value. using speed of sound formula, where v is the temperature, 25 degrees celsius in this case the speed of sound was theoretically calculated to be 332.34476. when compared to the average result of this experiment and using,[ (Theoritcal - Experimental)/0.5(Theoritcal + Experimental)] x 100. A percent error of 11.26351551%. this somewhat high percent error can be attributed to the in precise method of determining the time.

Speed of Sound Formula

Introduction to Sound

Introduction to Sound 

Objective:

 The objective in this lab was to analyze the periodicity of human sounds as well as the wave properties of  a human voice.

Equipment: 

Laptop

Logger Pro

Microphone

Procedure:

 To perform this lab a microphone was set up with logger pro. one persons voice was recorded saying "AAAAAA" and then analyzed for period and frequency. This was then repeated with a different subject. Finally the experiment was performed using a tuning fork.

First Voice:

Although this wave is not pretty it can be seen that it is periodic. It appears to show 4 waves based on a chosen point that represents the repetition. This sample's length can be likened to the blink of an eye. In order to determine the period the time between two "peaks" was measured by picking two pints where the wave appears to start over resulting in a period 0.0063 and a frequency of 158.7 hz based on f= 1/T . Using V= λf and 340 m/s as the speed of sound gives  a wave length of 2.142 m.

2nd Voice:

this voice showed a period of 0.0083 s and a frequency of 120.5 Hz and a wave length of 2.822 m .

There is a clear difference in the amplitude of the two voices.

Tuning Fork ( 570 Hz) :

the periodicity of these waves is much clearer than with the earlier ones. The second wave has a higher amplitude because it was struck on a harder surface. Analyzing the period of these waves resulted in a frequency of 256.41 Hz and the tuning fork is supposed to be 570 Hz, this shows that the equipment is quite accurate in its measurements. The shape of this graph when compared to the human voice shows that the human voice does not emit a constant sound. 

Standing Waves

Standing Waves

Objective: Understand driven standing waves and investigate resonant conditions for a standing wave.

Equipment:

Pasco Student Function Generator
Pasco Varible Frequency Wave Driver with String
50g weight hanger and slotted weight set
2 table clamps
a Pulley
Short Rod
Pendulum clamp
2 meter stick

Procedure:

Set up 

Set Up

 The length and mass of the string were measured in order to find the linear density,μ, of the string. M=0.00409kg, l=4.43m,so μ=mass per unit length=0.000923(kg/m). The system was then set-up. The string was held in two places on the table, one of which had a mass hung on it (0.250kg), Case 1. and went over the edge of the table via a pulley. The wave driver was attached to the string 2.00 ±0.02m away from the pulley. The wave driver was hooked up to the function generator. The frequency generator was then adjusted to obtain different harmonics in the string. the frequency and wave length was recorded for each harmonic. The procedure was then repeated with a different hanging mass ( 0.050 kg), Case 2 and thus a different tension.

Data Analysis:

Case 1 ( 0.250 kg)

After recording all the date for Case 1, frequency was graphed vs the inverse of wavelength (λ), in Microsoft Excel. This resulted in a linear graph with a slope equal to the velocity of wave propagation. this was also done for case 2 

Case 2 ( 0.050 kg)

Additionally, wave speed was calculated using :



This resulted in speeds of 51.5(m/s) for case 1 and 23.0(m/s) for case 2.
This was the compared to the slope values from the graphs which were 45.697(m/s) for case 1 and 20.81 (m/s) for case
Using the percent error formula gives an error of 12% for case 1 and the percent error for case 2 is 10%

The ratio of the experimental speeds for case one and case two is 2.20. When This is compared to the ratio of the calculated values of the wave speeds (which is 2.024) it is evident that the ratios of the two are nearly identical.

For case one when the ratio of the first and second harmonic frequencies is taken it comes to be 1.96 which is nearly double as it should be to follow the pattern f=nf0 where n is the harmonic number. The same follows for case two where the ratios of the first two harmonic frequencies is 2.19.

Error: There was minor error in the measurement of the mass and length of the rope that impacted the experiment. Another source of error came from finding the resonant frequencies. At some points (especially the higher harmonics) it was difficult to pinpoint the exact frequency that gave it the greatest amplitude. The values for the experimental wave speeds determined from the slopes of the graphs were very accurate and gave a r-squared value of 0.9997.

Fluid-Dynamics

Fluid Dynamics

Objective:  This labs objective was to use the Bernoulli equation to figure out the time it takes to drain an amount of water from a bucket with a hole in the bottom and use this to examine experimental error.

Equipment:
A bucket with a small hole drilled into the side
Tap water
Graduated cylinder
Ruler
Stopwatch


Procedure:

The procedure for this experiment consisted of taking the bucket of water and sealing off the hole. Then adding water to it until the desired height. A graduated cylinder is then used to measure the amount of time for a specific volume to exit the hole. This value is then compared to a theoretically calculated amount based on the given dimensions of equipment.

H of water

Bucket

Experiment

Resusts: After performing the experiment, an average time of 9.84 seconds was measured, this along with each individual trial is above 100% error when compared with the theoretical value obtained using the given diameter of the hole of 6.35 mm or 0.25 in. As a result of this an assumption was made that the given diameter was incorrect and using the given time equation along with some algebra the calculated diameter came out to be approximately 3 mm resulting in a percent error between the diameter's of 75%. This result shows that depending on the reported value of the drill bit used to make the hole, is not accurate enough to produce good results. The large amount of error can also be attributed to the assumptions made of this being an ideal case. This method assumes the final velocity will be sqrt(2gh).

Table of important data

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