Question

darcy suffers from farsightedness equally severely in both eyes. the focal length of either of darcy's eyes is 19.1 mm in its most accommodated state (i.e, when the eye is focusing on the closest object that it can clearly see) what lens strength (a.k.a., lens power) of contact lenses should be prescribed to correct the farsightedness in darcy's eyes? when wearing her contact lenses, darcy's corrected near point should be 2 5 . 0 25.0cm. (assume the lens-to retina distance of darcy's eyes is 2.00 cm, and the contact lenses are placed a negligibly small distance from the front of darcy's eyes)

Answer 1

Darcy should be prescribed contact lenses with a power of 56.36 diopters to correct her farsightedness and achieve a corrected near point of 25 cm.

Step-by-step explanation:

To determine the lens strength (or lens power) that Darcy would need to correct her farsightedness, we need to first assess the desired corrected near point and then calculate the required diopters (D) of lens power. Darcy's eye in its most accommodated state has a focal length of 19.1 mm (0.0191 m) but this doesn't provide clear vision at the desired distance. She wants to bring her near point to 25.0 cm (0.25 m), so this is her desired focal point when wearing contacts.

Using the lensmaker's equation (1/f = 1/do + 1/di), we replace di with the lens-to-retina distance (2.00 cm or 0.02 m) and solve for do (the distance from the lens to the object). However, since we prescribe contact lenses, we assume that they are close enough to the eye to not significantly change the focal length of the eye.

The lens formula can thus be rewritten as:

1/f = 1/do + 1/(-di) where di is negative since the image is formed behind the eye's lens. We can simplify this to:

1/f = 1/-0.0191 = -52.36 D (the available focal length of the eye without correction)

Now we add the required power for correction to bring the near point to 25 cm:

1/fdesired = 1/0.25 = 4 D (the desired focal length with correction)

This means we need to add power to the eye's existing focusing ability:

Lens Power Needed = fdesired - feye = 4 D - (-52.36 D) = 56.36 D

Darcy should be prescribed contact lenses with a power of 56.36 diopters to correct her farsightedness and bring her near point to 25 cm.