Object at focal point of converging lense

Khan, when an object is placed at the focal point of a converging lens, the image formed is at infinity. This can be explained through ray diagrams, where the rays parallel to the principal axis will pass through the focal point and the rays passing through the focal point will become parallel to the principal axis. This phenomenon is based on the lens equation, where the object distance becomes zero when the image distance is at infinity. In summary, when an object is placed at the focal point of a converging lens, the image formed is at infinity, and this can be demonstrated through ray diagrams and the lens equation.
  • #1
I have a simple question that I can't seem to answer...

why is it that when an object is at the focal point of a converging lense, the image is at infinity? How can you show this through ray diagrams?
 
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  • #2
admajoremdeigloriam said:
I have a simple question that I can't seem to answer...

why is it that when an object is at the focal point of a converging lense, the image is at infinity? How can you show this through ray diagrams?

The lens equation:

[tex]\frac{1}{f} = \frac{1}{i} + \frac{1}{o} [/tex]

What is the object distance if i = f? Or, what is the image distance if o = infinity?

AM
 
  • #3


When an object is placed at the focal point of a converging lens, the rays of light coming from that object will be parallel to the principal axis of the lens. This means that the refracted rays will also be parallel to the principal axis, and will not converge or diverge. As a result, the image formed by these refracted rays will appear to be at an infinite distance, or at infinity.

To demonstrate this through ray diagrams, we can draw three rays of light coming from the object towards the lens. The first ray will be drawn parallel to the principal axis and will pass through the focal point of the lens. The second ray will pass through the center of the lens and will not be refracted. The third ray will pass through the focal point on the other side of the lens and will emerge parallel to the principal axis.

These three rays will converge at a point on the other side of the lens, forming the image of the object. However, since the refracted rays are parallel to the principal axis, they will never actually meet at a point, giving the illusion that the image is at an infinite distance.

In summary, when an object is placed at the focal point of a converging lens, the refracted rays will be parallel to the principal axis, resulting in an image at infinity. This can be shown through ray diagrams by drawing three rays and observing how they behave after passing through the lens.
 

1. What is the focal point of a converging lens?

The focal point of a converging lens is the point on the principal axis where parallel rays of light converge after passing through the lens. It is the point where the lens focuses the light to form an image.

2. How is the focal point of a converging lens determined?

The focal point of a converging lens is determined by the curvature of the lens and its refractive index. The distance from the center of the lens to the focal point is known as the focal length, which is typically measured in meters.

3. What happens to the focal point if the distance between the object and the lens changes?

If the distance between the object and the lens changes, the focal point will also change. As the object moves closer to the lens, the focal point will move further away from the lens, and vice versa. This is known as the lens equation: 1/f = 1/do + 1/di, where f is the focal length, do is the distance from the object to the lens, and di is the distance from the lens to the image.

4. Can the focal point of a converging lens be outside the lens?

Yes, the focal point of a converging lens can be outside the lens. This is known as a virtual image. In this case, the rays of light do not actually converge at the focal point, but they appear to converge when extended back through the lens.

5. How does the shape of a converging lens affect its focal point?

The shape of a converging lens, specifically its curvature, can affect the focal point. A lens with a greater curvature or shorter focal length will have a closer focal point, while a lens with a flatter curvature or longer focal length will have a further focal point. This is why lenses with different shapes are used for different purposes, such as correcting nearsightedness or farsightedness.

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