What is the Speed of the Image in Optics?

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SUMMARY

The discussion focuses on calculating the speed of an image formed by a converging lens when the object moves towards it. The object is initially placed 20 cm from a lens with a focal length of 5 cm, moving at a speed of 12 cm/s. The lens formula, 1/f = 1/di + 1/do, is utilized to derive the relationship between object distance (do) and image distance (di) as functions of time. The solution involves applying calculus to find the derivative of the image distance with respect to time to determine the image's speed.

PREREQUISITES
  • Understanding of the lens formula: 1/f = 1/di + 1/do
  • Basic calculus concepts, particularly differentiation
  • Knowledge of object and image distances in optics
  • Familiarity with velocity calculations: v = d/t
NEXT STEPS
  • Study the application of calculus in optics, specifically in relation to lens equations
  • Learn about the behavior of converging lenses and image formation
  • Explore the concept of rates of change in physics
  • Investigate practical problems involving moving objects and lenses
USEFUL FOR

Students studying optics, physics enthusiasts, and anyone interested in understanding the dynamics of image formation through lenses.

Lara_C
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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?
 
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Lara_C said:

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
 
Thank you for your help!
 

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