Finding focal length from di v. M graph

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To find focal length from a di vs. M graph, the equation di = f + fM is not effective as it implies the slope and y-intercept are identical, which is incorrect. A more suitable rearrangement of the equation is f = di/(1+M), simplifying the calculation. This approach aligns better with the graph's structure and facilitates solving for focal length. The discussion emphasizes the importance of correctly interpreting the relationship between di and M. Accurate calculations are essential for understanding optical systems.
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Homework Statement
Using the di v. M graph, how would you find the focal length? The slope is 11.24. The y intercept is 8.753.
Relevant Equations
1/di + 1/do = 1/f
M = di/do
di = f (1+ di/do)
I tried di= f +fM, but that would mean slope and y int is the same when it’s not.
 
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If you rearrange your equation to f = di/(1+M) that might be easier to solve since your graph is di vs. M.
 
Thread 'Chain falling out of a horizontal tube onto a table'

Thread 'Chain falling out of a horizontal tube onto a table'

My attempt: Initial total M.E = PE of hanging part + PE of part of chain in the tube. I've considered the table as to be at zero of PE. PE of hanging part = ##\frac{1}{2} \frac{m}{l}gh^{2}##. PE of part in the tube = ##\frac{m}{l}(l - h)gh##. Final ME = ##\frac{1}{2}\frac{m}{l}gh^{2}## + ##\frac{1}{2}\frac{m}{l}hv^{2}##. Since Initial ME = Final ME. Therefore, ##\frac{1}{2}\frac{m}{l}hv^{2}## = ##\frac{m}{l}(l-h)gh##. Solving this gives: ## v = \sqrt{2g(l-h)}##. But the answer in the book...
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