Thin Lens Problem: Solving for Object Distance w/ Magnification

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In summary, the object must be placed at a distance of twice the focal length of the lens in order to produce a real image with a magnification of 2.00X. If the image is to be virtual, the object must be placed at a distance of twice the focal length of the lens and the virtual image will have a magnification of 2.00X.
  • #1
LastXdeth
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Homework Statement



(a) How far from a 50.0-mm-focal-length lens must an object be placed it its image is to be magnified 2.00X and be real?

(b) What if the image is to be virtual and magnified 2.00X?

Homework Equations



Thins Lens Equation: 1/f = 1/do + 1/di

Magnification Equation: M = hi/ho = -di/do

The Attempt at a Solution



I see that we're only given three pieces of information:
  • f=50.0mm
  • M=2.00
  • The image is real

However, I don't know how to incorporate the magnification equation with the Thins Lens Equation.
 
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  • #2
LastXdeth said:

Homework Statement



(a) How far from a 50.0-mm-focal-length lens must an object be placed it its image is to be magnified 2.00X and be real?

(b) What if the image is to be virtual and magnified 2.00X?

Homework Equations



Thins Lens Equation: 1/f = 1/do + 1/di

Magnification Equation: M = hi/ho = -di/do

The Attempt at a Solution



I see that we're only given three pieces of information:
  • f=50.0mm
  • M=2.00
  • The image is real

However, I don't know how to incorporate the magnification equation with the Thins Lens Equation.

Draw a ray trace - the answer is then obvious, and comes VERY quickley.
 
  • #3
LastXdeth said:

Homework Statement



(a) How far from a 50.0-mm-focal-length lens must an object be placed it its image is to be magnified 2.00X and be real?

(b) What if the image is to be virtual and magnified 2.00X?

Homework Equations



Thins Lens Equation: 1/f = 1/do + 1/di

Magnification Equation: M = hi/ho = -di/do

The Attempt at a Solution



I see that we're only given three pieces of information:
  • f=50.0mm
  • M=2.00
  • The image is real

However, I don't know how to incorporate the magnification equation with the Thins Lens Equation.

Have you drawn the ray trace yet?
 
  • #4
Thanks!

I have answered my own question mathematically.

Since the magnification is 2.00, di = (2)(do). I just plugged it in the lens equation to find do.
 
  • #5
LastXdeth said:
Thanks!

I have answered my own question mathematically.

Since the magnification is 2.00, di = (2)(do). I just plugged it in the lens equation to find do.

Did you get both the real image and virtual image answers?
 
  • #6
Yes, a virtual image would have a di = -2(do) because the virtual image is upright and in front of the lens.
 

Related to Thin Lens Problem: Solving for Object Distance w/ Magnification

1. What is a thin lens problem?

A thin lens problem refers to a type of optical problem that involves determining the position of an object in relation to a thin lens and its resulting image. This problem is commonly encountered in optics and physics studies.

2. How do you solve for object distance in a thin lens problem?

To solve for object distance in a thin lens problem, you can use the thin lens equation: 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the object distance, and di is the image distance. Rearranging this equation will allow you to solve for the object distance.

3. What is the magnification in a thin lens problem?

Magnification in a thin lens problem refers to the ratio of the size of the image to the size of the object. It can be calculated using the formula M = -di/do, where M is the magnification, di is the image distance, and do is the object distance.

4. What are the units for object distance and magnification in a thin lens problem?

The units for object distance and magnification in a thin lens problem are typically in meters (m) or centimeters (cm). It is important to use consistent units when solving for these values to ensure accurate results.

5. Are there any limitations to solving thin lens problems?

Yes, there are some limitations to solving thin lens problems. The thin lens equation assumes that the lens is thin and that the object and image are located on the principal axis of the lens. It also assumes that the lens is in air and that the light rays passing through the lens do not undergo significant refraction. Additionally, the thin lens equation only applies to thin lenses with a refractive index of 1, which is a close approximation for most lenses but not all.

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