Solve Magnifying Glass Image Distance w/ Focal Length 17cm +2.00 Mag

  • Thread starter mortho
  • Start date
  • Tags
    Reflection
In summary: Your name] In summary, to find the distance at which to hold a magnifying glass with a converging lens of focal length 17.0 cm to get an image with a magnification of +2.00, you can use the lens equation and the magnification equation to find the object distance, which is 11.33 cm. This means that the lens should be held 11.33 cm away from the nickel to achieve the desired magnification.
  • #1
mortho
100
0

Homework Statement


A magnifying glass has a converging lens of focal length 17.0 cm. At what distance from a nickel should you hold this lens to get an image with a magnification of +2.00?



Homework Equations


1/F=(1/Dobject)+(1/Dimage)
M=-Dimage/Dobject

The Attempt at a Solution



I did not know how to even start this because the distance of the image is not given so i cannot solve and plug. Please help, just started this lesson couple of days ago. Thanks!
 
Physics news on Phys.org
  • #2


Dear student,

Thank you for your question. Let's break down the problem step by step:

1. First, we need to understand what is meant by "magnification of +2.00". Magnification is a measure of how much an image is enlarged or reduced compared to the original object. A magnification of +2.00 means that the image is twice the size of the original object.

2. Next, we need to understand the relationship between focal length, object distance, and image distance for a converging lens. The equation you provided, 1/F=(1/Dobject)+(1/Dimage), is known as the lens equation. It tells us that the focal length (F) of a lens is equal to the inverse of the object distance (Dobject) plus the inverse of the image distance (Dimage). In other words, the focal length is the sum of the distances from the lens to the object and from the lens to the image.

3. Now, let's apply this equation to our problem. We know that the focal length of the magnifying glass is 17.0 cm. We also know that we want a magnification of +2.00. Using the magnification equation, M=-Dimage/Dobject, we can rearrange it to solve for Dimage: Dimage=-M*Dobject. Plugging in our values, we get Dimage=-2.00*Dobject. This means that the image distance is twice the object distance.

4. Since we are looking for the distance at which to hold the lens, we need to find the object distance. This is the distance from the lens to the object, which in this case is the nickel. We can use the lens equation to find this distance. Plugging in our known values, we get: 1/17.0=(1/Dobject)+(1/-2.00*Dobject). Solving for Dobject, we get Dobject=11.33 cm. This is the distance at which you should hold the lens from the nickel to get an image with a magnification of +2.00.

I hope this helps. If you have any further questions, please don't hesitate to ask. Good luck with your studies!
 
  • #3


I would suggest starting by understanding the concepts of focal length and magnification. The focal length of a lens is the distance from the lens to the point where parallel rays of light converge. In this case, the focal length of the magnifying glass is given as 17 cm. Magnification, on the other hand, is the ratio of the size of the image to the size of the object. In this case, the magnification is given as +2.00, which means the image will appear 2 times larger than the object.

Next, we can use the equations provided to solve for the distance of the object and the image. We know that the distance of the object (Dobject) is the distance from the object to the lens, and the distance of the image (Dimage) is the distance from the lens to the image. We also know that the magnification (M) is equal to -Dimage/Dobject.

Using the equation 1/F=(1/Dobject)+(1/Dimage), we can rearrange it to solve for Dimage:

1/Dimage = 1/F - 1/Dobject

Substituting the given values, we get:

1/Dimage = 1/17 - 1/Dobject

Since we know that the magnification is +2.00, we can substitute M = -Dimage/Dobject and solve for Dobject:

M = -Dimage/Dobject

2.00 = -Dimage/Dobject

Dimage = -2.00*Dobject

Substituting this into the equation for Dimage, we get:

1/Dimage = 1/17 - 1/(-2.00*Dobject)

1/Dimage = 1/17 + 1/(2.00*Dobject)

Now, we can substitute this into the equation 1/F = (1/Dobject) + (1/Dimage):

1/F = (1/Dobject) + (1/17 + 1/(2.00*Dobject))

1/F = (1/Dobject) + (1/17 + 1/(2.00*Dobject))

1/F = (2.00 + 1/17)* (1/Dobject)

1/F = (34/17)* (1/Dobject)

Dobject = 17/34 * F

Substituting the given focal length of 17 cm, we get:

Dobject = 17/34 *
 

1. What is the formula for calculating image distance using a magnifying glass with a focal length of 17cm and a magnification of +2.00?

The formula for calculating image distance is: 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, f = 17cm and the magnification (M) is +2.00, so we can rearrange the formula to solve for di: di = do/(M-1) = do/(2.00-1) = do/1 = do. Therefore, the image distance is equal to the object distance.

2. How do I determine the object distance if the image distance is 34cm when using a magnifying glass with a focal length of 17cm and a magnification of +2.00?

Using the same formula from question #1, we can solve for do: do = (f*di)/(f+di) = (17cm*34cm)/(17cm+34cm) = 578/51 = 11.33cm. Therefore, the object distance is 11.33cm.

3. Can a magnifying glass with a focal length of 17cm and a magnification of +2.00 be used to magnify objects that are farther than 17cm away?

No, a magnifying glass with a focal length of 17cm and a magnification of +2.00 can only magnify objects that are within 17cm of the lens. Objects that are farther away will appear smaller and out of focus.

4. How can I increase the magnification of a magnifying glass with a focal length of 17cm?

The magnification of a magnifying glass is determined by its focal length and the distance between the lens and the object. To increase the magnification, you can either decrease the focal length or move the lens closer to the object. However, keep in mind that the object must be within the focal length for the magnifying glass to work properly.

5. Can I use a magnifying glass with a focal length of 17cm and a magnification of +2.00 to view objects that are smaller than the lens?

Yes, a magnifying glass with a focal length of 17cm and a magnification of +2.00 can be used to view objects that are smaller than the lens. However, the object should be placed closer than the focal length for it to appear magnified and in focus.

Similar threads

  • Introductory Physics Homework Help
Replies
12
Views
7K
  • Introductory Physics Homework Help
Replies
10
Views
986
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
3K
Back
Top