Ordinary glasses are worn in front of the eye and usually 2.00 cm in front of the eyeball. A certain person can see distant objects well, but his near point is 60.0 cm from his eyes instead of the usual 25.0 cm. Suppose that this person needs ordinary glasses.
What focal length lenses are needed to correct his vision ?
Here's my work so far:
I think that since the near point is 60cm, the image should be at 60cm from the lens, but since the lens is worn 2cm from the eye, the focal length should be 60-2 so 58cm, right?
To determine the focal length of the lenses needed to correct the vision, we can use the lens formula:
1/f = 1/v - 1/u
Where:
f is the focal length of the lens
v is the image distance
u is the object distance
In this case, the object distance (u) is the distance between the lens and the eye, which is 2.00 cm. And the image distance (v) is the distance of the near point, which is 60.0 cm.
Using the formula:
1/f = 1/60 - 1/2
Simplifying:
1/f = (1 - 30)/60
1/f = -29/60
Inverting both sides:
f = -60/29
The focal length of the lens needed to correct the vision is approximately -2.07 cm. Keep in mind that the negative sign indicates that the lens is a diverging lens.