- #1

- 13

- 0

## Homework Statement

## Homework Equations

1/do+1/di=1/f

## The Attempt at a Solution

I tried finding the distance of image at 27m and then at 30.5m and taking the difference but that didn't work.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Dan453234
- Start date

- #1

- 13

- 0

1/do+1/di=1/f

I tried finding the distance of image at 27m and then at 30.5m and taking the difference but that didn't work.

- #2

jtbell

Mentor

- 15,866

- 4,451

- #3

ehild

Homework Helper

- 15,543

- 1,915

- #4

- 13

- 0

How would I perform the calculation with instantaneous speed?averagespeed of the image? I think their talking about "initial speed" indicates that they wantinstantaneousspeed.

- #5

- 13

- 0

I tried doing this but unfortunately this didn't give me the correct answer. Is there a more accurate way of doing this?

- #6

jtbell

Mentor

- 15,866

- 4,451

How do you get instantaneous speed (or more precisely, velocity) from position?How would I perform the calculation with instantaneous speed?

- #7

- 13

- 0

derivative?How do you get instantaneous speed (or more precisely, velocity) from position?

- #8

jtbell

Mentor

- 15,866

- 4,451

Yup.

- #9

- 13

- 0

Ok cool, I'm still a little confused how i would apply it to this problem however.Yup.

- #10

ehild

Homework Helper

- 15,543

- 1,915

What did you get? Yes, taking the derivative of di would be more accurate, but not much different.I tried doing this but unfortunately this didn't give me the correct answer. Is there a more accurate way of doing this?

- #11

jtbell

Mentor

- 15,866

- 4,451

I'm still a little confused how i would apply it to this problem

You know the relationship between ##d_0## and ##d_i##: $$\frac 1 {d_o} + \frac 1 {d_i} = \frac 1 f.$$ Take the derivative with respect to t, of both sides of this equation, and you'll have a relationship between ##\frac {dd_o}{dt}## and ##\frac {dd_i}{dt}##.

- #12

jtbell

Mentor

- 15,866

- 4,451

With Δt = 1 s I get about a 13% difference in the final answer, using the full precision of my calculator.taking the derivative of di would be more accurate, but not much different.

I agree, if Dan shows us his working, we can tell him if he at least calculated that approximation correctly.

- #13

ehild

Homework Helper

- 15,543

- 1,915

Yes, it is true.With Δt = 1 s I get about a 13% difference in the final answer.

- #14

jtbell

Mentor

- 15,866

- 4,451

Good luck... if I want to get up for work in the morning I need to go to bed now.

- #15

- 13

- 0

I am getting .00011 if i do it using the approximation with average velocity. It marks this as incorrect.With Δt = 1 s I get about a 13% difference in the final answer, using the full precision of my calculator.

I agree, if Dan shows us his working, we can tell him if he at least calculated that approximation correctly.

- #16

ehild

Homework Helper

- 15,543

- 1,915

The method with differentiation must be more accurate. Differentiate the equation ##\frac {1} {d_o} + \frac {1} {d_i} = \frac {1} {f} ## with respect to time and solve it for di'.

- #17

jtbell

Mentor

- 15,866

- 4,451

Yes, that's what I got. Another way to get more accuracy would be to use a smaller time interval. In principle, if you make it small enough, the answer will get close enough to the exact answer to make your software happy. But you have to be very careful to avoid roundoff errors.I am getting .00011 if i do it using the approximation with average velocity.

- #18

- 13

- 0

Great i ended up doing this and got the right answer. Thanks!Yes, that's what I got. Another way to get more accuracy would be to use a smaller time interval. In principle, if you make it small enough, the answer will get close enough to the exact answer to make your software happy. But you have to be very careful to avoid roundoff errors.

- #19

ehild

Homework Helper

- 15,543

- 1,915

Share: