Thin Lens Exp: Prove Linear Graph, Determine Slope and Intercept

[Kalashnikov]

Hi,

I'm first year Engineering in the Phys1130 course at my college and I've ended up hitting a large brick wall with the pre-lab. The pre-lab section of the experiment goes:

"The thin lens equation is:

(1/do) + (1/di) = (1/f)

di = distance from lens to image
do = distance from lens to object
f = focal distance from lens

Now, the pre-lab asks to prove that the plot of (dodi) vs (do + di) is linear and to determine what the slope and intercept are predicted to be.

Show that if two lenses (f1, f2) are placed together (assume distance between them is 0), the equivalent focal length of the system is given by:

(1/f) = (1/f1) + (1/f2)"

Alright, for the first half of the pre-lab I have rearranged the formula, added the intercept value of 'b' to the end of the equation but cannot seem to find out how to prove that its a linear graph. I know it should be, but I cannot find a way to communicate that across. The slope and intercept is also a mystery to me because we are given no values to calculate them with, unless of course the most we can do is algebra calculations.

the formula became: dodi = f(do + di) + b and from here I do not understand how to determine these values of slope and intercept as well as prove its a linear graph. Any hints or help would be GREATLY APPRICIATED

The second half of the pre-lab is almost blowing my mind. I was fairly confident I knew what I was doing, substituting in values for f1 and f2 and others, but I'm feeling almost nausiated thinking about other ways and whether or not my way is correct.

 

[vsage]

Compare the units of d0 + di and (d0*di).

 

[M98Ranger]

I'm assuming I have to prove that the two equations are equal to each other in some way, but I'm not sure how to go about it.

Thanks in advance for any help!

Hi there,

It sounds like you're struggling a bit with the pre-lab for your thin lens experiment. Don't worry, it can be a bit tricky at first but with some practice, you'll get the hang of it. Let's break down each part of the pre-lab and see if we can work through it together.

Firstly, for the first part where you need to prove that the plot of (dodi) vs (do + di) is linear, you're on the right track with rearranging the equation and adding an intercept term. To prove that the graph is linear, you need to show that it has a constant slope. This means that no matter what values you plug in for do and di, the ratio between dodi and (do + di) remains the same. This can be done by manipulating the equation and showing that it can be written in the form y = mx + b, where m is the slope and b is the intercept.

For the second part, where you need to determine the slope and intercept, you can use the same method as above. Plug in some values for do and di and see if you can find a pattern in the resulting values for dodi and (do + di). This will give you the slope and intercept of the linear graph.

As for the second half of the pre-lab, you are correct that you need to prove that the two equations are equal to each other. This can be done by substituting in values for f1 and f2 and showing that the resulting equations are the same. It might be helpful to try a few different values for f1 and f2 to see if the equation holds true for all cases.

I hope this helps and good luck with your experiment! Remember, don't be afraid to ask for help if you get stuck. Your classmates, TA, or professor are all great resources. Keep practicing and you'll get the hang of it.