Calculate the focal length of the spectacle lens

In summary, the task was to calculate the focal length of a spectacle lens needed to correct a hyperopic eye with a near point of 1.10 m, assuming the normal eye has a near point of 25.0 cm. Using the formula 1/f=1/p+1/q, the attempt at a solution used 0.25 m as p and 1.1 m as q, giving a focal length of 0.20 m. However, the correct answer is 0.324 m. The conversation also discussed the location of the image formed by the lens when the object is placed 25 cm away, with the conclusion that it should be on the opposite side of the lens and q is negative in this
  • #1
gungo
27
1

Homework Statement


A hyperopic eye has a near point of 1.10 m. Calculate the focal length of the spectacle lens required to correct the hyperopia (assume that the near point of the normal eye is 25.0 cm.)

Homework Equations


1/f=1/p+1/q

The Attempt at a Solution


I just used .25 m as p and 1.1 m as q and inverted it to solve for f, which gave me 0.20 m, but the answer given is 0.324 m.
 
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  • #2
In order for the person to be able to clearly see an object placed 25 cm away, where should the image of the object formed by the lens be located? Should the image be on the same side of the lens as the object?
 
  • #3
TSny said:
In order for the person to be able to clearly see an object placed 25 cm away, where should the image of the object formed by the lens be located? Should the image be on the same side of the lens as the object?
It should be on the opposite side, so q is negative,right? That would give the right answer.
 
  • #4
gungo said:
It should be on the opposite side, so q is negative,right? That would give the right answer.
q is negative when the image is on the same side as the object.

Try to draw a diagram showing the location of the person’s head, the lens, the object, and the image. You don’t have to post the diagram, but drawing it might help.
 

Related to Calculate the focal length of the spectacle lens

1. What is the definition of focal length?

Focal length is the distance between the lens and the point where all light rays converge to form a sharp image.

2. How is the focal length of a spectacle lens calculated?

The focal length of a spectacle lens can be calculated by dividing the lens power (in diopters) by 100. For example, a lens with a power of +2.00D has a focal length of 20 cm.

3. Can the focal length of a spectacle lens be changed?

Yes, the focal length of a spectacle lens can be changed by adjusting the lens power. A higher lens power will result in a shorter focal length, while a lower lens power will result in a longer focal length.

4. How does the focal length of a spectacle lens affect vision?

The focal length of a spectacle lens determines how light rays from an object are refracted to form an image. A shorter focal length will result in a more magnified image, while a longer focal length will result in a smaller, less magnified image.

5. Is the focal length of a spectacle lens the same for everyone?

No, the focal length of a spectacle lens varies for each individual depending on their prescription and the shape of their eye. It is important to have an eye exam and a personalized prescription to ensure the correct focal length for optimal vision correction.

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