A nearsighted person cannot read a sign that is more than 5.2 m from his eyes. To deal with thi

step 1 Using the lens equation, I can write the expression as 1 by f is equal to 1 by D0 plus 1 by D .I

A nearsighted person cannot read a sign that is more than...

A nearsighted person cannot read a sign that is more than $5.2 \mathrm{~m}$ from his eyes. To deal with this problem, he wears contact lenses that do not correct his vision completely, but do allow him to read signs located up to distances of $12.0 \mathrm{~m}$ from his eyes. What is the focal length of the contacts?

Key Concepts

Thin Lens Equation

The thin lens equation, given by 1/f = 1/v - 1/u, relates the object distance (u), the image distance (v), and the focal length (f) of a lens. This equation is fundamental in geometric optics for designing lenses and calculating the necessary focal length for vision correction.

Sign Conventions in Lens Equations

Sign conventions are crucial when using the thin lens equation to account for virtual versus real images. In corrective lens problems, object distances are typically positive, while the image distance for virtual images (which are needed for correcting vision in myopia) is taken as negative. This helps ensure that the resulting calculations yield the correct focal length and sign for the lens.

Corrective Lenses

Corrective lenses are used to adjust the focal point of the light entering the eye so that images form correctly on the retina. In cases of myopia, these lenses typically create a virtual image of a distant object at a distance where the patient can see clearly, effectively 'moving' the far point of the eye.

Near Point

The near point of a nearsighted person is the farthest distance at which the eye can clearly see objects without corrective lenses. It is a critical parameter in understanding myopia and is used to determine the corrective power required to adjust the focus of distant objects.

Myopia (Nearsightedness)

Myopia is an optical condition in which the eye focuses images in front of the retina instead of directly on it, causing distant objects to appear blurry. This condition is often described in terms of a 'far point', which is the maximum distance at which an object can be seen clearly by a nearsighted person.

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