[LENS] Given focal length and height, find object distance

In summary, to find the distance between an object and a convex mirror if the image height is 25% of the object height and the focal distance is 0.2m, we can use the equation 1/p+1/q=1/f, where p is the object distance, q is the image distance, and f is the focal distance. Solving for q, we get q=4p, meaning the distance from the object to the mirror is 4 times the distance from the image to the mirror.
  • #1
Phil123
1
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Homework Statement


An object is in front of a convex mirror. We then obtain an erect image whose height is equal to 25% of the height of the object. What is the distance between the object and the mirror if we know that the focal distance is equal to 0.2m?

Homework Equations


M = Yi/Yo = q/p
1/p+1/q=1/f

Yi= height of the image
Yo = height of the object
q = distance of the image
p= distance of the object
M = magnification
f = focal distance

The Attempt at a Solution



M = Yi/Yo = 0.25 since the image is 25% the height of the object.
Then, since M=q/p, I know the distance from the object to the mirror is 4 times the distance of the image to the mirror.
This is where I'm stuck.
 
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  • #2
Phil123 said:

Homework Statement


An object is in front of a convex mirror. We then obtain an erect image whose height is equal to 25% of the height of the object. What is the distance between the object and the mirror if we know that the focal distance is equal to 0.2m?

Homework Equations


M = Yi/Yo = q/p
1/p+1/q=1/f

Yi= height of the image
Yo = height of the object
q = distance of the image
p= distance of the object
M = magnification
f = focal distance

The Attempt at a Solution



M = Yi/Yo = 0.25 since the image is 25% the height of the object.
Then, since M=q/p, I know the distance from the object to the mirror is 4 times the distance of the image to the mirror.
This is where I'm stuck.
Use the equation you included 1/p+1/q=1/f. Take care of the signs of focal length and image distance.
 

FAQ: [LENS] Given focal length and height, find object distance

1. How do you calculate the object distance of a lens given the focal length and height?

To calculate the object distance of a lens, you 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. Rearrange the equation to solve for do: do = 1/(1/f - 1/di). This will give you the distance between the object and the lens.

2. What is the relationship between focal length and object distance?

The relationship between focal length and object distance is inverse, meaning as the focal length increases, the object distance decreases. This means that a longer focal length will result in a closer object distance, and a shorter focal length will result in a farther object distance.

3. Can the object distance be negative in this equation?

Yes, the object distance can be negative in the thin lens equation. This indicates that the object is located behind the lens, meaning it is on the same side as the observer. A negative object distance is common in cases where the lens is used as a magnifying glass or in a microscope.

4. How do you use the height of the object in this equation?

The height of the object is not directly used in the thin lens equation. However, it can be used to determine the image height, which is needed to calculate the magnification of the lens. The magnification equation is m = hi/ho = -di/do, where hi is the image height and ho is the object height. The negative sign indicates that the image is inverted compared to the object.

5. What are some real-world applications of this calculation?

This calculation is commonly used in photography to determine the appropriate distance between the camera and the subject for a desired focal length. It is also used in the design of optical instruments such as telescopes and microscopes to produce clear and magnified images. Additionally, it is used in the manufacturing of eyeglasses to determine the correct lens power for a person's prescription.

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