In order to clearly read a book 16 cm away, a farsighted girl needs an image to be 36 cm from her eyes. What focal length is needed for the lens in her eyeglasses?
28.56
To find the focal length needed for the lens in the girl's eyeglasses, we can use the lens formula:
1/f = 1/v - 1/u
Where:
f is the focal length of the lens,
v is the distance of the image from the lens, and
u is the distance of the object from the lens.
In this case, the object (the book) is 16 cm away from the girl's eyes, so u = -16 cm (negative since it is on the opposite side of the lens). The image should be 36 cm from her eyes, so v = -36 cm (negative since the image is formed on the opposite side of the lens as well).
Now, let's substitute these values into the lens formula:
1/f = 1/-36 - 1/-16
Simplifying the equation:
1/f = -16/(-36*-16) - 36/(-16*-36)
1/f = 1/576 - 1/576
1/f = 0
The equation simplifies to 0. Therefore, the focal length needed for the lens in the girl's eyeglasses is infinity. This means that the lens should have no power to correct the girl's farsightedness. Instead, the lenses in her eyeglasses may be used to protect her eyes or correct other visual impairments.