Finding Distance Between Lens Positions: Solve for a

  • Thread starter dmolson
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In summary, the problem involves finding the distance between two positions of a lens, given the focal length and the fixed distance between the object and its image. To solve this, we use the lens equation and the fact that the sum of the object and image distances is equal to the fixed distance.
  • #1
dmolson
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Homework Statement



The distance between an object and its image is fixed at 40.0 cm. A converging lens of focal length f = 4.2 cm forms a sharp image for two positions of the lens. What is the distance a between these two positions?

Homework Equations



1/p + 1/q = 1/f

The Attempt at a Solution



I am very confused with this problem and really have no idea where to begin. If anyone can provide some assistance, that would be great. Thanks.
 
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  • #2
You have the lens equation. You know f. You also know that p+q=40. So what you have is two equations and two unknowns. Try solving for p (or q) and see what you come up with.
 
  • #3


As a scientist, my first suggestion would be to draw a diagram of the situation. This will help you visualize the problem and identify any key information that may be missing. From the given information, we know that the distance between the object and its image is 40.0 cm and the focal length of the lens is 4.2 cm. We also know that the lens forms a sharp image for two positions. This means that the image is formed at the same distance from the lens, regardless of the position of the lens.

Using the thin lens equation, 1/p + 1/q = 1/f, we can solve for the distance a between the two positions of the lens. Since the image distance q is the same for both positions, we can set up the equation as follows:

1/p + 1/q = 1/f

1/p + 1/q = 1/4.2 cm

We can rearrange this equation to solve for p, the distance from the object to the lens:

1/p = 1/4.2 cm - 1/q

p = 4.2 cm / (1/4.2 cm - 1/q)

Now, we know that the distance between the object and its image is 40.0 cm, so we can substitute q = 40.0 cm into the equation:

p = 4.2 cm / (1/4.2 cm - 1/40.0 cm)

p = 4.2 cm / (0.238 cm - 0.025 cm)

p = 4.2 cm / 0.213 cm

p = 19.7 cm

Since the distance a between the two positions of the lens is the difference between the object distance p and the focal length f, we can calculate a as:

a = p - f

a = 19.7 cm - 4.2 cm

a = 15.5 cm

Therefore, the distance a between the two positions of the lens is 15.5 cm.
 

What is the formula for finding the distance between lens positions?

The formula for finding the distance between lens positions is a = (s2 - s1) / (1 - (s1 / f)).

What do the variables in the formula represent?

The variable "a" represents the distance between the lens positions, "s1" represents the distance of the first lens position from the object, "s2" represents the distance of the second lens position from the object, and "f" represents the focal length of the lens.

Can this formula be used for any type of lens?

Yes, this formula can be used for any type of lens as long as the focal length is known.

What units should be used for the variables in the formula?

The units for "a", "s1", and "s2" should be consistent, whether it is in meters, centimeters, or millimeters. The focal length "f" should also be in the same units as the distances.

What is the significance of finding the distance between lens positions?

Finding the distance between lens positions is important in determining the optimal placement of lenses for creating the desired image. It can also help with troubleshooting and adjusting the position of lenses for better image quality.

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