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AN630078
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- Homework Statement
- Hello, I have a question below which I am rather uncertain how to approach concerning an investigation into the lens formula, I have attached the table of results from the question also. I am especially stumbling on sections of the question concerning uncertainty and would be very grateful of any help. I have attempted to answer all of the questions, and in places where there are an absence of solutions I have explained where I am stuck.
Sorry this is rather a lengthy post, clearly the questions lead on from another which is why I have posted them collectively in case amending one section may advance another area which I am having difficulty with. Thank you to anyone who replies.
In an experiment, students varied the distance (u) between a point source of light and a lens, and measured the corresponding distance (v) from the lens to a screen on which a real image was formed. The students found a range of positions on the screen for each distance u for which the image looked quite sharp. The students chose to record the the smallest and largest possible values of v for each value of u.
Question 1.
ii Suggest a reason why any uncertainty in the values of u can be neglected.
ii. Describe the variation in the uncertainty shown by v
Question 2
i. Draw a table of the values of 1/u and the largest and smallest values of 1/v.
ii. Plot the data from your table in a graph of 1/v against 1/u. Include error bars and add a straight line of best fit.
iii. Use the graph to find the focal length of the lens.
- Relevant Equations
- 1/u+1/v=1/f
y=mx+c
Question 1.
i Suggest a reason why any uncertainty in the values of u can be neglected.
I am really rather unsure how to answer this question but I have produced my opinion nonetheless.
One could assume that the uncertainty in object distance u, i.e., the distance from the lens to the light source is very small compared to the uncertainty of the image distance, i.e., the distance from the lens to the image formed on the screen.
This yields an object uncertainty of such a small magnitude that it becomes negligible and can be omitted.
Question 1 ii. Describe the variation in the uncertainty shown by v
I truly do not know how to answer, is this referring to the difference in the largest and smallest image distances?
If this is correct, then the variation in the uncertainty shown by the image distances greatly decreases as the object distance increases, for example this difference decreases from 0.2m at an object distance of 0.22m to 0.14m when u=0.28 to 0.03 m when u=0.33 etc.
Question 2
i. Draw a table of the values of 1/u and the largest and smallest values of 1/v.
I have calculated the reciprocal of the original values and presented these in a table which I have attached to 3.s.f.
ii. Plot the data from your table in a graph of 1/v against 1/u. Include error bars and add a straight line of best fit.
I do not have trouble in plotting this graph, however, I am uncertain of the the values to plot for the reciprocal of the image distance (1/v), would this be the average of the smallest and largest image distances?
i.e. when 1/u=4.54 m, would 1/v=(1.12+0.917)/2=1.019 m to 3.s.f ?
Also, I do not know how to include error bars in my graph, I have not been taught to do so. I know that percentage uncertainty= absolute error/measurement * 100%
The absolute uncertainty would be ±0.5 mm if a ruler was used with a resolution of 1mm.
How would this be applicable, if at all, to producing error bars. I have read my textbook but it does not explicate this at all, only the difference between random and systematic errors. Although I have also looked online I have not found a great deal of resources on how to produce error bars, and admittedly what I have found has been a little confounding and not especially applicable to this scenario.
iii. Use the graph to find the focal length of the lens.
Once I have produced my graph, I can compare the lens formula 1/u+1/v=1/f with that for a straight line graph; y=mx+c.
Clearly, the y-intercept of the graph will be the reciprocal of the focal length.
i Suggest a reason why any uncertainty in the values of u can be neglected.
I am really rather unsure how to answer this question but I have produced my opinion nonetheless.
One could assume that the uncertainty in object distance u, i.e., the distance from the lens to the light source is very small compared to the uncertainty of the image distance, i.e., the distance from the lens to the image formed on the screen.
This yields an object uncertainty of such a small magnitude that it becomes negligible and can be omitted.
Question 1 ii. Describe the variation in the uncertainty shown by v
I truly do not know how to answer, is this referring to the difference in the largest and smallest image distances?
If this is correct, then the variation in the uncertainty shown by the image distances greatly decreases as the object distance increases, for example this difference decreases from 0.2m at an object distance of 0.22m to 0.14m when u=0.28 to 0.03 m when u=0.33 etc.
Question 2
i. Draw a table of the values of 1/u and the largest and smallest values of 1/v.
I have calculated the reciprocal of the original values and presented these in a table which I have attached to 3.s.f.
ii. Plot the data from your table in a graph of 1/v against 1/u. Include error bars and add a straight line of best fit.
I do not have trouble in plotting this graph, however, I am uncertain of the the values to plot for the reciprocal of the image distance (1/v), would this be the average of the smallest and largest image distances?
i.e. when 1/u=4.54 m, would 1/v=(1.12+0.917)/2=1.019 m to 3.s.f ?
Also, I do not know how to include error bars in my graph, I have not been taught to do so. I know that percentage uncertainty= absolute error/measurement * 100%
The absolute uncertainty would be ±0.5 mm if a ruler was used with a resolution of 1mm.
How would this be applicable, if at all, to producing error bars. I have read my textbook but it does not explicate this at all, only the difference between random and systematic errors. Although I have also looked online I have not found a great deal of resources on how to produce error bars, and admittedly what I have found has been a little confounding and not especially applicable to this scenario.
iii. Use the graph to find the focal length of the lens.
Once I have produced my graph, I can compare the lens formula 1/u+1/v=1/f with that for a straight line graph; y=mx+c.
Clearly, the y-intercept of the graph will be the reciprocal of the focal length.