Quick Question about lenses/refraction

  • Thread starter JamesL
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In summary, a concave lens with a distance of 7.9cm between the object and the image forms a virtual image that is 0.5 times the size of the object. By using the lens equation and a consistent sign convention, we can find the focal length of the lens to be a negative value.
  • #1
JamesL
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A concave lens forms a virtual image .5 times the size of the object. The distance between the object and the image is 7.9cm.

Find the focal length of the lens. Answer in units of cm.
------------

i suppose what is confusing me is whether or not the object itself is virtual. i don't see how (with a concave lens) a real object could produce a virtual image smaller than itself.

i can construct a series of equations for this problem fairly easily, but I am not doing it correctly apparently.

anyway, if i consider the object itself to be virtual, both Id and Od (image distance and object distance would be negative)...

so:

.5 = -(-Id)/(-Od)
Od = -2Id **

-Od - Id = 7.9 cm **

focal length f = ((1/-2Id) - (1/Id))^-1 **

the equations with asteriks were the ones i used... am i setting them up correctly?

any help is appreciated.
 
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  • #2
sign convention

JamesL said:
anyway, if i consider the object itself to be virtual, both Id and Od (image distance and object distance would be negative)...
But there's no reason to assume a virtual object. Assume the usual real object and let the equations do the work. But you'd better use a consistent sign convention: if you want Id to be a positive number, then the image distance is -Id; similarly, the object distance (assumed real until proven otherwise) is the positive number Od.

so:

.5 = -(-Id)/(-Od)
Od = -2Id **
0.5 = - (-Id)/(Od)
Od = 2Id

-Od - Id = 7.9 cm **
Od - Id = 7.9 cm
Thus: Id = 7.9 cm; Od = 2(7.9) cm

Now use the lens equation to find the focal length (which better turn out negative!):
1/f = 1/Od + 1/(-Id)
... etc

(Tip: Draw yourself a picture.)
 
  • #3


Hi there, it seems like you are on the right track with your equations. To find the focal length of the lens, we can use the thin lens equation: 1/f = 1/di + 1/do, where f is the focal length, di is the image distance, and do is the object distance.

In this case, we know that the image distance is 7.9 cm and the object distance is negative since it is virtual. So, we can plug in these values to get:

1/f = 1/7.9 + 1/-Od

Now, we also know that the image size is 0.5 times the object size, so we can use the magnification equation: m = -di/do = hi/ho, where m is the magnification, hi is the image height, and ho is the object height.

In this case, since the image is virtual, we can say that hi is negative and ho is positive. So, we can write:

-0.5 = -7.9/Od

Solving for Od, we get Od = 15.8 cm.

Now, going back to our thin lens equation, we can plug in this value for Od and solve for f:

1/f = 1/7.9 + 1/-15.8

Solving for f, we get f = -11.85 cm.

Since the focal length is a distance, we can say that the focal length is 11.85 cm.

Hope this helps clarify things for you! Let me know if you have any other questions. Happy to help!
 

1. How does the shape of a lens affect refraction?

The shape of a lens plays a crucial role in refraction, as it determines the degree to which light is bent as it passes through the lens. Convex lenses, which are thicker in the middle and thinner at the edges, cause light rays to converge and focus. Concave lenses, which are thinner in the middle and thicker at the edges, cause light rays to diverge.

2. What is the difference between a converging and diverging lens?

A converging lens, also known as a convex lens, causes light rays to bend and converge at a single point after passing through it. This point is known as the focal point. In contrast, a diverging lens, also known as a concave lens, causes light rays to spread out and diverge after passing through it.

3. How does the index of refraction affect the bending of light?

The index of refraction is a measure of how much a material can slow down the speed of light. The higher the index of refraction, the more a material can bend light. For example, glass has a higher index of refraction than air, which is why light bends when it passes through a glass lens.

4. What is the difference between refraction and reflection?

Refraction and reflection are both ways in which light can change direction. Refraction occurs when light passes through a material and bends, while reflection occurs when light bounces off a surface without passing through it. Refraction is responsible for the formation of images by lenses, while reflection is responsible for the way we see objects in a mirror.

5. How is the focal length of a lens determined?

The focal length of a lens is determined by its shape and curvature. A lens with a shorter focal length will cause light rays to converge more quickly, while a lens with a longer focal length will cause light rays to converge more slowly. The focal length can also be adjusted by changing the distance between the lens and the object being viewed.

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