Optics: Thin Lenses - Determining Focal Length

[genevievelily]

Homework Statement

In the photo (which I cannot post now, but it is a magnifying glass, and a dollar bill) the images through the lens appears twice the size and it is at a distance of 3.0cm from the lens of the magnifying glass. Determine focal length.

Homework Equations

1. -di/do=m
2. 1/f=1/di+1/do

The Attempt at a Solution

Since twice the size m will be 2. Using equation 1:

di=-m*do
= -2*3.00cm
= -6.00cm

This makes sense since image is upright and virtual, and in lenses virtual images are negative.

When I calculate focal length,

1/f=1/-6+1/3
f=6

But this answer is wrong the answer is 3. What am I doing wrong or what do I not understand?

Thanks!

 

[TSny]

Homework Statement

In the photo...the images through the lens appears twice the size and it is at a distance of 3.0cm from the lens of the magnifying glass. Determine focal length.

Perhaps the word "it" here refers to the image rather than the object.

 

[Basic_Physics]

The answer is clearly wrong. If the object was placed on the suggested focal point, 3 cm, the image would be real and located at infinity.

 

[TSny]

You will get the right answer if you interpret the distance of 3.0 cm as the magnitude of the distance from the lens to the image.

 

[Nickie]

Hello, thank you for your question. I understand that you are trying to determine the focal length of a magnifying glass based on the image size and distance. Your attempt at using the thin lens equation was a good start, but there are a few things that need to be corrected in order to get the correct answer.

First, when using the thin lens equation, it is important to use consistent units. In this case, your image distance and object distance are both given in centimeters, so your focal length should also be in centimeters. Therefore, the correct equation to use is 1/f = 1/di + 1/do, where di and do are both in centimeters.

Next, the magnification factor (m) should be positive since the image is upright. This means that the equation should be di = m*do, where m = 2 in this case.

Using these corrections, the equation becomes 1/f = 1/6 + 1/3, which gives a focal length of 3 cm, as you correctly stated.

I hope this helps clarify the issue and shows the importance of using consistent units and considering the sign of the magnification factor in the thin lens equation. Keep up the good work in your studies!