Lab 11: CD Diffraction (12-04/10/2012) *

Lab Partner: Adhitya, Bryan 

Purpose:

In this experiment we will be determining the grating spacing of a CD disc by diffracting a laser beam. We will examine the calculated grating by comparing the determined value with the standard CD disc grating distance and determine the validity of the calculation and method.


Method and Calculation:

 

Figure 1: Experiment apparatus for laser diffraction 

Table 1: Theoretical Value for Lab Equipment

Wavelength of Laser (nm)

632.8

 

 Figure 2: Performing measurement from the diffraction plate to the observed pattern

Table 2: Measured Value

Distance from Diffraction Plating to the Observed Pattern (cm)	45.2 ± 0.05
Distance between diffraction maxima m = 0 to m = 1 (cm)	21.25 ± 1.25

Table 3: Calculation for Diffraction Grating

Angle between the diffraction maxima m = 0 and m = 1 (o)	25.18 ± 1.25*
Calculated Grating Spacing (nm)	1487.33 ± 20.8*

Table 4: Evaluation of Result

Theoretical Value of Diffraction Spacing (nm)	1600
Calculated Grating Spacing (nm)	1487.33 ± 158.8*
Percent Error (%)	7.04

Conclusion:

In this lab, we have determined the grating spacing for a standard CD disc by employing the concept of diffraction grating. We have obtained a result of 7.4 percent raw error and a zero percent error under the uncertainty. We argue that our calculation remain valid as the determined value of grating spacing is in the uncertainty range.

Lab 10: Lecture Lab (04/05/2012) s

Purpose: 

To measure the thickness of human hair using interference pattern in electromagnetic 

waves.

Method:

In this lab we will examine the interference pattern when a laser passes a hole separated by a piece of hair. Using the equation λ = (d*y)/L we will be able to calculate d, the diameter of the hair, by measuring y, the spacing of interference pattern, and L, the distance between the laser and the interference pattern. This experiment procedure is valid because the thickness of the hair is within the magnitude of the wavelength of the laser beam.    

Figure 1: Laser generator.

Figure 2: Interference pattern of the laser. 

Data and Analysis:

Table 1: Measurements of interference pattern.

Y (mm)	L (m)	λ (nm)
6.5 ± 0.2	1 ± 0.02	632.8

Figure 3: Calculation for the diameter of hair.

d = (λ*L)/y 

= (632.8 * 10^-9) / (6.5 *10^-3)

= 97 μm

     Uncertainty: 

μd = (μλ*μL)/μy

= 63 μm

Table 2: Thickness of hair.

Laser (μm)	Micrometer (μm)
97 ± 63	70 ± 30

Conclusion:

In this lab we have calculated the diameter of a piece of hair using the interference equation. We believe our data to be accurate under the uncertainty as 97±63 μm is under the range of human hair thickness under a variety of sources (http://hypertextbook.com/facts/1999/BrianLey.shtml).  We also believe that optical determined thickness for small object is superior to manually measuring the thickness using a micrometer. 

Lab 9: Lenses (10-04/03/2012) x

Purpose:

In this lab we will examine the physical property of thin lens to determine the characteristic and behavior of lens.


Method:

We will find the relationship between the image distance and object distance by measuring the magnification of the lens on several points. The set will be graph to analyze and deduce the general behavior of the lens.

di (cm)	1/di	do (cm)	negative 1/do
7.1	0.140845	25	-0.04
7.3	0.136986	20	-0.05
8.4	0.119048	15	-0.066666667
10.7	0.093458	10	-0.1
15.7	0.063694	5	-0.2

di (cm)	do (cm)
7.1	25
7.3	20
8.4	15
10.7	10
15.7	5

Figure : Inverse Image Distance vs Negative Inverse Object Distance

y = 0.481x + 0.1547

Conclusion:

We find that the relationship of inverse image distance relative to negative inverse object distance is directly proportional to each other. The linear line of both grapg evidences this general relationship. Thus the lens equation 1/p +1/q = 1/f holds true. 

Lab 8: Concave and Convex Mirrors (9) s

Purpose:

The purpose of this lab is to examine the property of concave and convex mirrors and derive the ray diagram for the corresponding mirrors.

Method:

• In this lab we will observe the image produce by convex and concave mirror by varying the distance between the object and the mirror. We will also determine the significance of focal length and curvature property of the mirror to determine the orientation and property of the image.

Figure 1: Convex Mirror

• The image produce by the convex mirror has similar orientation to the object but is decrease in size. The image dimension will decrease when the object distance increase.

Figure 2: Concave Mirror

• The image produce by the concave mirror is upright if the image is inside the radius of curvature, however the image is inverted when the object distance is outside the radius of curvature

Figure 3: Convex Mirror Ray Diagram

Figure 4: Concave Mirror Ray Diagram

Conclusion:

In this lab we have examined the behavior of concave and convex mirrors by summarizing the actions of light through ray diagram. We evidences and validates the general behavior of image production by analyzing the reflection of light rays on the surface of mirrors. We found that convex mirror can only produce upright and virtual image that is smaller than the real object. This behavior is due to the location of the focal length. Since the object distance cannot penetrate the vertex and exceed the focal point the image is outside of the curvature and focal length. However in a concave mirror, the image is more complex. When the object distance decrease, the image became upright and smaller. When the object distance increase, the image became bigger and inverted. The transition between these two behavior is located on the radius of curvature and focal length. The behavior is logical as the light ray in concave mirror behaves according to the reflection equation. 

Lab 7: Lab Quiz (3/22/2012) s

Question: 

A microwave oven is in the back of the class room. We have placed some marshmallows in the microwave to make some measurements of the standing wave. Determine the frequency of this microwave. From this deduce a range of possible dimensions for microwaves including the smallest possible microwave. In this lab we also microwaved a cup of water. What is the total energy content of the captivity? How many photons per second are oscillating in the microwave? What pressure do these photons exert on the side of the microwave?

Data:

• Distance between peak energy: 12 ± 1cm
• Estimate mass of water: 100 ± 1g
• Change in water temperature: 37 ± 1 ^oC 
• Dimension of Microwave in W*L*H:  (36 ± 1cm) *(36 ± 1cm)*(23 ± 1cm)

Method:

 

Figure 1: Microwave and marshmallow used in this lab.

Analysis:

• The measured distance between peak energy also represents the distance between two adjacent anti-nodes. Thus  λ can be calculate by multiplying 2 to the distance.
• λ = d * 2
•  Since the microwave must contain the entire wavelength, the dimension of the microwave must be a positive integer multiple of the wavelength. 
•  width =  m * λ,  length =  n * λ ,    whereas n and m is positive integer
• the smallest dimension would be when n and m equal one
• The energy in captivity is in direct relationship with the change of temperature
• E = mcΔT
• The numbers of proton can be find by dividing the total energy in captivity to the energy a proton holds.
• Energy of a proton in microwave: E = hf
• c = f λ,     f =  λ / c 
• Pressure on the side is directly proportional to Poynting vector and speed of light
• P = S / c (assuming the microwave is black body)
• S ≈ I,      in which I = intensity = power/area
• power = E / t  

 

Figure 2: Calculation for wavelength, frequency, energy and number of photons.

Table 1: Wavelength and frequency

λ (m)	f (Hz)
0.24 ± 0.01	1.25*109

Table 2: Possible Dimension

Width (m)[ j Є Z+]	Length (m) [ k Є Z+]
0.24 * j	0.24 * k

Table 3: Energy and power.

Total Energy (J)	Power (W)	Energy per proton (J/proton)
15481 ± 200	516 ± 16	(8.29 ± 0.04)*10-25

Table 2: Photon and pressure.

Number of photons (photon)	Pressure (Pa)	Photon per Second (photon/s)
(1.87 ± 0.06)*1028	(1.33 ± 0.048)*10-5	(6.23 ± 0.02)*1026

Conclusion:

In this lab we have discussed the behavior of electromagnetic standing wave through analyzing the physical properties of the microwave. We found that the dimension of the microwave have to include the wavelength of the microwave spectrum. Thus the dimensions of a microwave will always be an integer multiple of the wavelength.

Lab 6: Lecture Lab (3/16/2012) s

Purpose:

In this lab we will measure the angular velocity of a spinning pipe in two distinct harmonic to deduce the length of the pipe.


Method:

We will determine the modes of a harmonic through solving the unknown n  by equating the length of the pipe represent by L = n(λ/2) and L = (n+1)*(λ/2). The wavelength will be measure through the angular velocity of the pipe using logger pro. Once n is determined, we can substitute the mode into the length equation to calculate L.


Data and Analysis:

 

Figure 1: Calculation of the length of the pipe. 

ƒ = ω/ 2π

λ = v / ƒ 

μ ƒ  = μω/ 2π

μλ = (v / ƒ_max) - (v / ƒ_min)

Table 1: Measurements from spinning pipe

Harmonic	ω(rad/s)	ƒ(Hz)	λ(m)
Low	3859 ± 0.51	614.49± 0.08	0.5598 ± 0.000145
High	5068 ± 1.10	807.01 ± 0.18	0.425 ± 0.0000845

Figure 2: Calculation of the length of the pipe. 

L = (n₁ / 2) *λ₁

L = ((n₁+1) / 2) *λ₂

n₁ = 3.1 ≈ 3 

(Harmonics are whole numbers)

Substitute n

and

μL =  (μλ / 2) * 3

L = 0.8397 ± 0.0002175 m

Conclusion:

In this lab we have determined the length of the pipe by measuring the angular velocity of two distinct harmonics. The length of the pipe is inversely related to the frequency of the harmonics. Thus by equating the two standing wave equation in terms of length we were able to determine the n of the harmonics and deduce the length of the pipe. We have calculated our uncertainty by setting an upper and lower bound on the calculations. The range between the bound will serve as the uncertainty. We believe that the error in the can be entirely attribute to the precision of the lab equipment.