The near point of an eye is 48.5 cm. A corrective lens is to be used to allow this eye to focus clearly on objects at the distance of the healthy near point. What should be the focal length of this lens


The focal length of the lens should be -51.5 cm (a concave lens).


The purpose of the lens is to make objects at 48.5 cm appear at the healthy near point. The healthy near point is 25.0 cm.

We use the lens formula

\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}

where f = focal length, u = object distance and v = image distance.

In this case, u = 48.5 cm and v = -25.0 cm.

v is negative because the image is virtual an not real. (Here, we are using the real-is-positive sign convention)

\dfrac{1}{f} = \dfrac{1}{48.5} + \dfrac{1}{-25.0} = -\dfrac{23.5}{1212.5}

f = -51.5

The negative sign indicates the lens is concave.

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