We are given , where
f=1 and q=4. We must find dp/dt.
Differentiate wrt time:
Solve for dp/dt:
We know q=4 and we can find p by
We do not know dq/dt. Were you given that?. Assuming I read the problem correctly.
Okay, so I have this question that has been killing me. This is it:
If f is the focal length of a convex lens and an object is placed at a distance p from the lens, then its image will be at a distance q from the lens, where f , p , and q are related by the lens equation
1/f=1/p+1/q
What is the rate of change of p with respect to q if q=4 and f=1 ?
So I've tried about a million approaches and I never get the right answer. I know you're supposed to show how you've attempted this problem, but I've tried so many ways I don't know which one to type on here. Basically, I'm hoping somebody will be able to give me a boot in the right direction because I actually haven't a clue as to how to even begin attacking this.
Any hints?
Thanks!
So I just figured it out. In case anybody is curious, here's how it's done:
Use the steps suggested by galactus:
"f=1 and q=4. We must find dp/dt.
"
Then differentiate with respect to q.
1/p=-(1/q)+1
(-1/(p^2))(dp/dq)=1/(q^2)
dp/dq=(1/q^2))/(-1/(p^2))
Simplifies to dp/dq=-(p^2)/(q^2)
if we solve
for p, we end up with p=[1/(1-(1/q))]
plug that into
dp/dq=-(p^2)/(q^2)
for p and plug in q=4 and we end up with (-1/9)
Yay!
Thanks for your help. You basis was vital in helping me figure this out. Sooo happy!!