What Is the Focal Length of Veronique's Glasses for Clear Vision?

[phy112]

Homework Statement

Veronique is nearsighted; she cannot see clearly anything more than 6.50 m away without her contacts. One day she doesn't wear her contacts; rather, she wears an old pair of glasses prescribed when she could see clearly up to 8.00 m away. Assume the glasses are 2.0 cm from her eyes.

a. What is the focal length of Veronique's glasses?
b. What is the greatest distance an object can be placed so that she can see it clearly with these glasses?

Homework Equations

1/p-1/q=1/f

The Attempt at a Solution

I literally have no idea where to start. any hints appreciated

 

[phy112]

so i got -7.98 for the focal length. but i don't know how to do b

 

[nlightner]

I can provide some insights and guidance on how to approach this problem.

First, let's define some key terms and concepts related to the focal length of glasses. The focal length of glasses refers to the distance between the center of the lens and the point where light rays converge to form a clear image on the retina of the eye. It is typically measured in meters or centimeters.

In this scenario, we know that Veronique is nearsighted, which means she has difficulty seeing objects that are far away. This is because the light rays from distant objects converge in front of her retina, resulting in a blurry image. To correct her nearsightedness, she wears glasses that help to diverge the light rays before they reach her eyes, allowing them to converge properly on her retina.

Now, let's look at the given information. We know that Veronique can see clearly up to 8.00 m away with her old glasses. This means that the focal length of her glasses must be such that the light rays from an object 8.00 m away converge on her retina. We also know that she can see clearly up to 6.50 m away without her contacts. This means that the focal length of her glasses must be such that the light rays from an object 6.50 m away converge on her retina when she wears them.

Using the equation 1/p-1/q=1/f, we can find the focal length of Veronique's glasses. We know that p=8.00 m and q=6.50 m, so we can plug these values into the equation and solve for f. This will give us the focal length of her glasses.

Once we have the focal length, we can use the same equation to find the greatest distance an object can be placed so that Veronique can see it clearly with her glasses. This would be the value of p in the equation, with q being the distance at which she can see clearly (6.50 m).

I hope this helps to get you started on solving this problem. Remember to always define your variables, use the appropriate equations, and double-check your calculations for accuracy. Good luck!