Focal Length of the phone camera lens PDF

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Focal Length of the phone camera lens The first formula that you must use is the equation of magnification where m= y prime/y = -s/s prime. We can calculate -s by measuring it using the ruler and we can calculate the height of the object by using the ruler again and also the height of the image can be calculated by the formula y prime = s(Py2 -Py1) where s is the pixel size of the smartphone sensor and Py2 and Py1 is the vertical direction of the pixel position in the ruler image and s can be calculated based on the image distance s prime the height of the image y prime and the height of the object y by using the thins lens equation 1/s – 1/s prime =1/f prime where we need to find f prime which is the focal length of the formula. For a camera lens systems, we could make an assumption that the camera lens that we use is converging. To be able to conduct this experiment we need to have a ruler to measure the object distance which is the object to the lens and we need to have a mobile phone to measure the sensor, we also used the ruler to measure the height of the object and the height of the image which is calculated in pixel and also the physical size of a sensor. You can also find all this information from the manufacturer website which we will need to find the focal length using the formula above.

Object distance

Image distance

To start the experiment we need to use a ruler and put it 100mm away from the camera lens -u, we also pick the ruler from the 2cm to 3cm and set them as the height of the lens in which we have 10mm and we can take measurement of the pixel position on the smartphone by using photoshop or they can also be taken from the manufacturer website and then we will have enough information to find the focal length of the image produced by the mobile phone. We could have systematic error or random error. Systematic error is when same error repeat for every measurement you take which means that you learned nothing by repeating the experiment and other method are needed to estimate uncertainties like different measurement or different calculation, random error is when you get different random result when repeating the experiment this mean the more experiment you measure the better the average will be and also estimation will be greatly accurate. The best wat to avoid estimate uncertainties is to collect as much data as you can and the you can be confident about the result. Measurement

Object distance s

Object Height y

Image Height y prime

Image distance s prime

Focal Length f （mm）

1 2 3 4 5

40 45 50 55 60

2.50 2.70 2.60 2.65 2.80

400 420 440 460 480

45 50 55 60 70

21.2 23.7 26.2 28.7 32.3

26.4+/-3.86 is the uncertainty of the focal length using the error proganda method I used.

We can tell from the straight line that the image distance has an inverse proportion with the image height. We can use the equation m=1/f to find focal length which is equivalent to f=1/m so f=1/9521 f= −4

1.05∗10 mm

8. We can tell that the focal length that we calculated are not what I expected from what I have from the phone specification this could be caused by the image height value is a lot higher than the image distance due to the information I gathered online.

9. to improve the result of the experiment we could take more measurement to make a more accurate reading and also see the trends more clearly and we can also increase the distance between the ruler and the camera lens to have a wider angle lens and use snail law to test what is the relationship 10. We could have an experiment where we increase the distance between the ruler and the camera lens to have a wider lens and we can use this to find out what happened to the focal length and also whether the relationship still holds...