A nearsighted person has a far point located only 200 cm from his eyes. Determine the focal length of contact lenses that will enable him to see distant objects clearly.
does anyone have any suggestion on how to tackle this problem?
jij
To determine the focal length of contact lenses, we can use the lens formula:
1/f = 1/v - 1/u
where:
f = focal length of the lens (unknown)
v = image distance (distance of the far point from the lens) = 200 cm
u = object distance (distance of the near point from the lens) = infinite (for a distant object)
Since the person is nearsighted, we need to correct their vision to see distant objects clearly. In this case, the near point is the object distance, which is typically taken as 25 cm.
Now we can substitute the known values into the lens formula and solve for f:
1/f = 1/v - 1/u = 1/200 - 1/25
To simplify the calculation, we need to find a common denominator for 200 and 25, which is 200. Thus:
1/f = (1/200)(25/25) - (1/25)(8/8) = 25/5000 - 8/200 = (25 - 40) / 5000 = -15/5000 = -3/1000
Multiplying both sides of the equation by -1000 to get rid of the fraction:
-1000/f = -3
Simplifying, we find:
f = -1000 / -3 = 333.33 cm
Therefore, the required focal length of the contact lenses for the nearsighted person is approximately 333.33 cm.
To determine the focal length of contact lenses that will enable a nearsighted person to see distant objects clearly, 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 (distance from the lens to the focused image)
- u is the object distance (distance from the lens to the object)
In this case, the far point for the nearsighted person is located only 200 cm from their eyes. This means that the object distance (u) is 200 cm.
Since we want the person to see distant objects clearly, the image distance (v) should be at infinity (∞).
Substituting these values into the lens formula, we have:
1/f = 1/∞ - 1/200
Since 1/∞ is essentially zero, the equation simplifies to:
1/f = -1/200
To find the focal length (f), we can rearrange the equation:
f = -200/1
Therefore, the focal length of the contact lenses that will enable the nearsighted person to see distant objects clearly is -200 cm (or 200 cm concave lenses). The negative sign indicates that the lens should be diverging (concave) to correct for the nearsightedness.