How Does Small y and d Affect the Difference Between r2 and r1 in Physics?

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SUMMARY

The discussion centers on the mathematical relationship between r1 and r2 in physics, specifically how small values of y and d influence their difference. The equations provided are r1 = √(L² + (y - 0.5d)²) and r2 = √(L² + (y + 0.5d)²). The conclusion reached is that in the limit where both y and d are significantly smaller than L, the difference r2 - r1 simplifies to yd/L. The participant also mentions using the binomial approximation for further simplification.

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Homework Statement



r1 = √(L2+(y-0.5d)2)
r2 = √(L2+(y+0.5d)2)
Show that in the limit that both y and d are <<L r2 - r1 = yd/L

Homework Equations


The Attempt at a Solution



r2 - r1 =(√(L2+(y+0.5d)2)) - (√(L2+(y-0.5d)2))

Nevermind, I've figured it out but can't seem to be able to delete this post :s
 
Last edited:
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I'd have tried substituting x=[(y-0.5d)/L]2 and used the binomial approximation.
Oh you figured it out - rather than delete the post - how about posting your result: that way others who get stuck can benefit.
 

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