mini project (optics)

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Department of Physics Faculty of Science & Mathematics Universiti Pendidikan Sultan Idris Vibrations, Waves & Optics (SFT 3023) MINI PROJECT REPORT -Focal Length and Magnification Of A Concave Mirror- Name : 1. Siti Saufu Bt Mat Isa (D20091035140) 2. Noramira Bt Ahmad Tajuddin (D20091035139) 3. Nor Awaathif Bt Mohd Ghazali Lee (D20091035070) Lecturer Name : Mr. Wan Zul Adli B. Wan Mokhtar EXPERIMENT TITLE

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Page 1: Mini Project (Optics)

Department of PhysicsFaculty of Science & Mathematics

Universiti Pendidikan Sultan Idris

Vibrations, Waves & Optics

(SFT 3023)

MINI PROJECT REPORT

-Focal Length and Magnification Of A Concave Mirror-

Name :

1. Siti Saufu Bt Mat Isa (D20091035140)

2. Noramira Bt Ahmad Tajuddin (D20091035139)

3. Nor ‘Awaathif Bt Mohd Ghazali Lee (D20091035070)

Lecturer Name : Mr. Wan Zul Adli B. Wan Mokhtar

Page 2: Mini Project (Optics)

EXPERIMENT TITLE

Focal Length and Mirror Magnification of a Concave Mirror

OBJECTIVE

1. To determine the focal length of a concave mirror.

2. To measure the magnification for a certain combination of object and image distances.

APPARATUS

1. Light Source

2. Bench

3. Concave Mirror

4. Half-screen

5. Metric Ruler

THEORY

Figure 1: Ray diagram of image formed by concave mirror when object beyond 2f

do

di

Page 3: Mini Project (Optics)

For a spherically surface curved mirror, the equation given:

1f= 1

do+ 1

d i (Eq 1)

Where f is focal length, do is the distance between the object and the mirror, and d i is the distance

between the image and the mirror. By measuring do and d i , the focal length can be determined.

Magnification, M, is the ratio of image size to object size. If the image is inverted, M is negative.

For magnification:

M =

image sizeobject size =

image distanceobject distance

PROCEDURE

PART A: Object At Infinity

Figure 2: The apparatus set up

Half ScreenConcave Mirror

Holder

Half Screen

Page 4: Mini Project (Optics)

Figure 3: Half screen

1. Set up the apparatus as shown in Figure 2.

2. Use concave mirror to focus the image of a distant object (the window or building next

door) on the half screen.

3. Move the half screen away from light source towards the concave mirror until a clear

image is formed on the half screen.

4. Find the distance of clear image, di formed on the half screen.

5. Record the value of di obtained.

Note: In this part,the focal length of the mirror could be determined by making a single

measurement of d i with do≃∞ .

PART B: Object Closer Than Infinity

Figure 4: The apparatus set up

1. The apparatus is set up as in Figure 4.

2. Place the light source and the mirror on the optics bench 50 cm apart. Make sure that the

light source’s crossed-arrow object is placed towards the mirror and the concave side of

the mirror is placed towards the light source.

3. Locate the half screen in front of the light source.

Half Screen

Light Source Concave Mirror Holder

do

di

Object

Page 5: Mini Project (Optics)

4. Slide the half screen away from the light source to a position where a clear image of

crossed-arrow is formed.

5. Measure the distance and record the data in Table 1.

6. Repeat step 2-5 with object distances of 45 cm, 40 cm, 35 cm, 30 cm and 25 cm.

7. Measure the object and image distance for mirror located 25 cm from the light source.

Measure the object and image size between two opposite points on the crossed-arrow

diagram.

RESULTS

PART I: Object at Infinity

Image distance, d i = 15.5 cm

By using equation 1,

1f= 1

do+ 1

d i

1f= 1

∞ + 115 .5

f = 15.5 cm

As do approaches infinity, what does 1

do approach?

As do approaches infinity, 1/do will approaching 0.

Page 6: Mini Project (Optics)

PART B: Object Closer Than Infinity

do d i1

do

1d i

Image Size Object Size

50.0 cm 22.9 cm 0.0200 0.0437

45.0 cm 24.4 cm 0.0222 0.0410

40.0 cm 26.0 cm 0.0250 0.0385

35.0 cm 28.7 cm 0.0286 0.0348

30.0 cm 32.5 cm 0.0333 0.0308

25.0 cm 41.3 cm 0.0400 0.0242 3.1 cm 2.0 cm

Table 1: Results taken from experiment

Figure 5: Image formed when do = 25 cm

Page 7: Mini Project (Optics)
Page 8: Mini Project (Optics)

ANALYSIS DATA

PART A: FOCAL LENGTH

1. Calculate 1/do and 1/di for all six rows in Table 1.

From equation 1,

1f= 1

do+ 1

d i

By rearranging it,

1do

=1f− 1

d i

1do

=− 1di

+ 1f( Eq 2)

Thus by comparing Equation 2 with general straight line equation,

y = mx + c

We obtained;

y =

1do

m = -1

x= 1d i

Page 9: Mini Project (Optics)

c= 1f

2. Plot 1/do versus 1/di and find the best-fit line (linear fit). This will give a straight line

with the x-intercept and y-intercept equal to 1/f. Record the intercepts (including

unit) here:

y-intercept = 1/f = 0.065 cm-1

3. For each intercept, calculate a value of f and record it in Table 1.

For y-intercept:

1/f = 0.065 cm-1

f = 15.385 cm

4. Find the difference between these two values of f and record them in Table 1.

For y-intercept:

Percentage difference = |15 . 0−15 . 87315 . 0

|×100 %

= 5.6%

5. Find the percent difference between this value and the focal length that you found in

part A. Record this data in Table 2.

f (cm)

Result from y-intercept 15.873

% difference between results from intercepts y-intercept: 5.6%

Result from Part A 15.5

Page 10: Mini Project (Optics)

% difference between results from y-intercept and result from

Part A

2.4%

Table 2: Results from graph plotted

PART B: MAGNIFICATION

1. For the last data point only (do= 25 cm), use the image and object distances to

calculate the magnification, M. Record the result in table 3.

M=−( dido )

By applying above equation, the value of M calculated is:

do=25 . 0cm

di=41.3 cm

M=−(41 . 3 cm25 . 0 cm )

M=−1 . 7

2. Calculate the absolute value of M using your measurement of the image size and

object size. Record the result in table 3.

|M|= image size

|M|= 3.1 cm

Object size

2.0 cm

Page 11: Mini Project (Optics)

|M|= 1.6

3. Calculate the percentage difference between the absolute values of M found using

both methods. Record the result in Table 3.

Theoretical value of magnification:

f= 15.0 cm

do=25.0 cm

1f= 1

do+ 1

di

115

= 125

+ 1di

di= 37.5 cm

M=−( dido )

M=−(37 . 5 cm25 . 0 cm )

M=−1 . 5

M calculated from image and object distances 1.7

Percentage difference 13.3 %

Table 3 (a): Magnification

(Theoretical value)

Page 12: Mini Project (Optics)

Percentage difference = | theoretical value - experimental value

theoretical value|

= |1. 5-1 . 7

1 . 5|X 100%

M calculated from image and object sizes 1.6

Percentage difference 6.7%

Table 3 (b): Magnification

Percentage difference =| theoretical value - experimental value

theoretical value|¿ 100 %

= |1.5-1 . 6

1 . 5|¿ 100%

=6.7 %

QUESTION

1. Is the image formed by the mirror upright or inverted?

Inverted.

2. Is the image real or virtual? How do you know?

Real because the image formed by the mirror is inverted.

3. By looking at the image, how can you tell the magnification is negative?

The image formed is inverted.

4. You made three separate determinations of f (by measuring it directly with distant

object, from the x-intercept of your graph, and from the y-intercept). Where these

three values equal? If they were not, what might account for the variation?

X 100 %

= 13.3 %

Page 13: Mini Project (Optics)

f by measuring directly with distant object = 15.5 cm

f from the y-intercept = 15.873 cm

These three values are not exactly the same but they are only slightly different in values

due to parallax errors. The image that had been seen by the experimenter might not be the

most clear one. The clear image might form a little bit in front or behind the measurement

taken.

DISCUSSION

From the experiment that have been conducted, there are several values of focal length that had

been obtained by using different method. Firstly is by measuring directly with distant object the

focal length measured is 15.5 cm. Second method is by plotting a graph of 1/do versus 1/di. The

line of the graph was being extrapolated to obtain its y-intercept that can be used to calculate the

focal length. From the y-intercept, the focal length calculated is 15.873 cm.

The theoretical value of focal length of concave mirror that we used is 15 cm. The percentage

difference of y-intercept is 5.6%. From the data collected, the most precise method is by

measuring it directly with distant object. As the percentage different for focal length measured

from distant object is;

|15 .0−15 . 515 .0

|×100 %

=3.33 %

These different values of focal length obtained is due to some errors occurred during the

experiment taken. In this experiment, the image distance, di is taken from the concave mirror to

where the image formed is the clearest one. The image seen by experimenter might not been the

clearest one and thus the image distance, di measured is not the exact one. Besides, the half

screen used in this experiment is home-made which is made by the experimenter due to no

appropriate screen available in the lab. For concave mirror, image will be formed in between the

object and mirror, thus the screen should not block the light that transmitted towards the mirror.

In this case, the screen provided is too long where it blocks the light from reaching mirror. Hence

student made their own half screen but the screen is adjusted manually where at times it is not

Page 14: Mini Project (Optics)

positioned exactly vertical and static as the screen provided because it cannot be tighten as the

screen provided. Therefore the actual image distance, di might be a little bit in front or behind

the measured distance. As the precaution, students should take several measurements and then

take their average as the data. Besides, the respesctive party can provide a shorter screen

compared to the one which already provided.

As for magnification of the image, students also used two methods to calculate the

magnification. First is by using the image and object distances, the magnification calculated is -

1.7. Meanwhile the second method is by using the image and object size with the magnification

calculated is 1.6. The most precise way is by using the image and object size as it caused less

percentage difference, 6.7% compared to magnification using image and object distances, 13.3%.

Errors that might contribute to this variation is due to several errors. First method is by

calculating it from the image and object distances measured. When experimenter took inaccurate

measurement in the first place (the errors are as stated in paragraph above), thus it also affected

the magnification calculated from these measurement. The second method is by measuring it

directly from image size formed. As for the object size, it does not give much problem as it

already fixed and student faced no problem in measuring it. But, error occurred when it comes in

measuring image size. Experimenter might wrongly marked the head and tail of the crossed-

arrow image formed, and thus affected the measurement of image size and consequently

magnification calculated. Other than that, the screen also contribute to this error because since it

is home-made and not exactly vertical. When experimenter wanted to mark on the screen, it

moves here and there a little bit and causes the marks are not acurate.

Therefore, as precaution students should take several measurements and calculated the average.

In concave mirror for object distance of 2f < di < f, the image will be formed behind the object.

Therefore, student can use the screen provided in the laboratory since it will not block the light

from reaching concave mirror. This is because student can stands the screen properly and the

screen also will not move here and there since it has screw that can be tighten on the bench.

CONCLUSION

1. The focal length of the concave mirror that we managed to get is 15.5 cm.

Page 15: Mini Project (Optics)

2. The magnification of the image formed by using the image distance and object

distance is -1.7.

3. The image formed is real and inverted.

REFERENCES

Anonymous (2011). Concave Mirror. Accessed from

http://www.splung.com/content/sid/4/page/concavemirrors on March 3, 2011.

Giancoli C. (2000). Physics for Scientist & Engineers with Modern Physics. USA: Prentice Hall.

Vuille and Serway (2009). College Physics. USA: Brooks and Cole.