What is the Speed of the Image in Optics?

[Lara_C]

Homework Statement

An object is placed 20cm from a converging lens of focal length 5cm. If the object moves towards the lens at a speed of 12cm/s, at what speed does the image move away from the lens?

Homework Equations

1/f=1/di+1/do
v=d/t

The Attempt at a Solution

Let's say the object moves...
Do=do1+do2
Di=di2-di1
so if di+fdo/do-f
vt=(fdo2/do2-f)-(fdo1/do1-f)
However, both vi and ti are unknown, so how should I proceed?

 

[ehild]

Homework Statement

An object is placed 20cm from a converging lens of focal length 5cm. If the object moves towards the lens at a speed of 12cm/s, at what speed does the image move away from the lens?

Homework Equations

1/f=1/di+1/do
v=d/t

The Attempt at a Solution

Let's say the object moves...
Do=do1+do2
Di=di2-di1
so if di+fdo/do-f
vt=(fdo2/do2-f)-(fdo1/do1-f)
However, both vi and ti are unknown, so how should I proceed?

Hi Lara, welcome to PF.

Have you studied some Calculus? The object moves towards the lens so the object distance is do=20-12t in terms of time. The velocity of the object is d(do)/dt=-12 cm/s. The velocity of the image is vi=d(di)/dt. In the lens equation, both do and di are functions of the time. Find the derivative of di at time t=0 when do = 20 cm.

ehild

 

[Lara_C]

Thank you for your help!