What is the Speed of the Image in Optics?

In summary, the problem involves an object placed 20cm from a converging lens with a focal length of 5cm. The object moves towards the lens at a speed of 12cm/s, and the question is what speed does the image move away from the lens. Using the lens equation and the formula for velocity, it is possible to find the derivative of the image distance at time t=0, when the object distance is 20cm. This will give the velocity of the image.
  • #1
Lara_C
2
0

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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  • #2
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
 
  • #3
Thank you for your help!
 

Related to What is the Speed of the Image in Optics?

1. What is the "speed of the image" in optics?

The speed of the image refers to how quickly an image is transmitted through a medium, such as air or water, and is often measured in meters per second. In optics, this refers to the speed at which light travels through a material, which can vary depending on the properties of the material.

2. How is the speed of the image related to the speed of light?

The speed of light is the fastest possible speed at which any object or information can travel. In most cases, the speed of the image is directly related to the speed of light, as light is the primary source of transmitting images in optics. However, the speed of light can vary depending on the medium it travels through, which can also affect the speed of the image.

3. Does the speed of the image change in different materials?

Yes, the speed of the image can vary depending on the properties of the material it is traveling through. For example, light travels slower through denser materials, such as glass, compared to less dense materials, such as air. This is due to the way light interacts with the atoms and molecules in the material.

4. How does the speed of the image affect the quality of an image?

The speed of the image can affect the quality of an image in several ways. If the speed is too slow, the image may appear blurry or distorted. This can happen when light is refracted or scattered as it travels through a medium. Additionally, the speed of the image can also impact the time it takes for an image to be transmitted, which can affect the perception of moving images.

5. Can the speed of the image be changed or controlled?

In some cases, the speed of the image can be controlled or manipulated. This can be achieved through the use of lenses, mirrors, and other optical instruments that can change the path of light. Additionally, certain materials, such as fiber optics, are specifically designed to control and maintain the speed of light and the resulting images. However, the speed of light itself cannot be changed or controlled.

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