hi- I have a problem I can't seem to get right. here it is.
"A retired bank president can easily read the fine print of the financial pages when the news paper is held no close than arm's length, 66.4 cm from the eye.
What should be the focal length of an eyeglass lens that will allow her to read at at the more comfortable distance of 23.3 cm? answer in units of cm"
When I tried to solve this I used the 1/do + 1/di= 1/f
then 1/66.4 + 1/23.3 =1/f and solved from there
however that must not be correct because I got it wrong.
please help!
The di stays the same, since it is determined by eyeball dimensions and indexes that do not change. Adding an eyeglass close to the eye adds additional curvature to the wavefront, so that the original 1/f of the eye's lens alone becomes 1/f = 1/f' + 1/f', where f' is the focal length of the eyelass lens.
You have to make use of the rule that the effective 1/f length of two closely spaced lenses is the sum of the 1/f values of the two individual lenses. 1/f is measured in units called "diopters", or m^-1
The new situation is
1/23.3 + 1/di = 1/f + 1/f'
The former situation was
1/66.4 + 1/di = 1/f
Subtracting the two,
1/f' = 1/23.4 - 1/66.4 = 0.02768 cm^-1
f' = 36.1 cm = 0.361 meters
This would be called a 1/.361 m^-1 or 2.8 diopter lens. You can buy them off the rack at drug stores.
ah thank you so much!!!
To solve this problem correctly, you need to use the lens formula, which is correct. The lens formula is given by:
1/f = 1/do + 1/di
Where:
- f is the focal length of the lens
- do is the object distance (in this case, the distance at which the newspaper is held from the eye)
- di is the image distance (in this case, the distance at which the newspaper appears to be in focus)
Let's solve the problem step by step:
1. Convert the object distance and image distance into meters:
- do = 66.4 cm = 0.664 m
- di = 23.3 cm = 0.233 m
2. Plug the values into the lens formula and solve for f:
1/f = 1/do + 1/di
1/f = 1/0.664 + 1/0.233
1/f = 1.51 + 4.29
Now, we add the fractions on the right-hand side of the equation:
1/f = 5.80
To isolate f, we take the reciprocal of both sides:
f = 1/5.80
Evaluating this value gives us:
f ≈ 0.1724 m
3. Convert the result back to centimeters:
f ≈ 0.1724 m * 100 = 17.24 cm
Therefore, the focal length of the eyeglass lens should be approximately 17.24 cm to allow the retired bank president to read at a more comfortable distance of 23.3 cm.