Measuring a human hair

we are to accurately measure the thickness of a human hair, not by a ruler but by the idea of double slit.  We can use the distance between the hair and the board, the interference y_m of the slit as well as overtones.

we first make a hole in a 3x5 card and taped a human hair on to it, than we pointed a laser through the hole, we used the image to be projected oh to the white board, we now can measure the distance between the board, and the distance between the middle of the zero overtone and third.  

from what we learned in class about double slit, we can derive an equation 

 

y_m=L(lambda)(m)/d

but we are looking for d

d=L(lambda)(m)/y_m

where y_m is the distance between the zero overtone and the m we picked

L is the distance between the hair and the white board

d is the thickness of the hair

y_m we got to be about 6.5 cm _+ .023cm

L = 2m

we used the third overtone m=3

and the wavelength of the laser is 660nm

applying the data to the equation above we get d to be about 6.09 *10^-5 and 6.27*10^-5

from this picture we can clearly see the interference of the double slit experiment, we are getting a bright slit then a dark slit, bright  meaning the waves are converging, while the dark slits are diverging, we can also see that the bright slits are going to be brighter on the inside and as it gets closer to the out side it gets darker.

analysis

by taking looking at this experiment we can assume that there is a lot of mistakes that can be made during the processes of the experiment.  measuring the distance of y_m might be the biggest, but compare that number to that of L, the mistakes is minimum.  the focus of this experiments is to show that light can be shown as a wave rather then particles.    

Lens

from what we observed from the mirrors and lens labs we can find out where the focal length of the lens is measuring it or by using the eq

                                                              1/s+1/s`=1/f
the focal point of the lens is the point where the parallel beam refract to.  after the beams hits the surface
we measured f equals 14.97cm



by using a double convex mirror we can increase distance between the object and mirror by a factor of the focal length, to produce different images smaller and larger depending on how far the object is from the   double convex mirror.

d_0 cm	d_i cm	h_i cm	h_0 cm
79.88	23.45	1.3	3
59.88	24.5	1.75	3
39.98	28.7	1.95	3
29.99	44.5	5.2	3
22.96	332.5	53.6	3

 if we change the object distance to about .5 the focal length the image would become to large for us to see, so we would assume that as the lens become closer to the object the image we receive is going to get larger.
if we look through the lens at the object and view the image when the focal length .5, we the the image upright and big.


analysis
from the experiment we observed that the image is always inverted, along both the vertical and  horizontal axis, if this was a single convex mirror then the image would not have have been inverted.



the two lens are going to have a different length in R, if we take that in to considerations we get

1/R1+1/R2=1/s+1/s`


the slope of the negative inverse d_0 to the negative inverse d_i is about .565 this would be the degree M that the image is changing.  like we observed if the object was getting further away then the image would become smaller and smaller till it becomes to small to measure.

Concave and Convex Mirrors

In this experiment, we are to show the different effects of a convex mirror vs a concave mirror.

when we stand in front of  a convex mirror, the image appears to be smaller than the object itself, it does however stays upright, and is located about the same position inside and outside the mirror.

when the object is moved closer to the mirror the image becomes bigger, and when it is moved further away the image gets smaller.

for the convex mirror we gotten the object height to be around 3.1cm+_.034cm

the distance of the object about 6.2cm+_.45cm

the image height about .7cm+_.23cm

and the image distance to be 2.3cm+_.31cm

we are given an equation for M which equals h_i/h_0 which gets you M = 0.2258

there is no units for M it is just a scalar number

PartII

now we can look at concave mirrors, the image that appears in the mirror is larger, but it is inverted, and relative to the position of the mirror the object well seem closer.

moving the object closer to the mirror makes the image smaller, and upright and as for moving further away the image grows to infinite 

for the concave mirror we gotten the object height to be around 3.1cm+_.034cm

the distance of the object about 6.2cm+_.45cm

the image height about 1.7cm+_.23cm

and the image distance to be 2.3cm+_.31cm

again we get M to be about .463+_.012 (no units)

my sketch is a little off on the height of the image, but that could have been me measuring it wrong, but the difference wouldn't matter.

analysis

in this experiment we can clearly see how convex and concave mirrors would work on an object being placed in front of them, we also identified how we can see the image in the mirror by drawing lines to where the focal point, the lens of the mirror and the center of the sphere.  knowing that we can find the height of the image, with the magnification of the object.

                                                                 m= - s`/s
                                             from this we can find m then we can use m to find y
                                                                  m= y`/y

introduction to Reflection and Refraction

in this experiment we are to show how light bends though a straight and curved surface. the relationship between the reflection angle, refraction angle, and the index of refraction. 

Experiment

Light box or laser, Semicircular plastic or glass prism, Circular protractor, pasco optical kit or hardtl disk

first, we use light strike at the flat surface of the semicircular plastic, and then we change the angle every t 10 degree every time we move the light until 70 degree to get the incidence angle and the refracton angle, and calculate sine value of them.

the data we revived from the first set of data is when light is on the flat side of the lens, we can see that the change of the angle that we measured  is changing linearly to the sin(incidence) and sin(refraction).  when we try to go pass 80 % the sin(incidence) and sin(refraction) become undef, this happens if the light is trapped in the lens.

the graph is to show the change of the reflection angle, and the change of the refraction angle.

for the second part of the experiment, we view the light going in through the curved side of the lens, which effects the angle of refraction not quite linearly any more, it is more like its going 1/x^2, but the light does gets trapped inside the lens, a lot faster then when the light is going through the straight side first.

The light ray may become dimmer when it enter curved surface of the semicircular prism as there is some amount of light ray reflected at the curved surface. The light ray travels from lower density to higher density from air to plastic and higher density to lower density from plastic to air. 

we were not able to complete all 10 trials, the angle of refraction got too small for us to take data with visible light.

analysis

form this experiment we can see that the effect of reflection and refraction on the light through a different medium at an angle.partI of the lab showed that the relationship of the reflection and refraction was linear,due to the flat surface of the lens, partII of the lab focused on the curved side, and the refraction angle changed proportion  to the reflection angle by 1/x^2.  no light escapes from the lens after about 40 degrees change in the incidence angel.