Question

There are three types of conditions by which the eye can not focus properly; myopia, hyperopia and astigmatism. Here we will explore only myopia and hyperopia. In myopia (for various reasons) the image within the eye focuses on a point in the vitreous humor and not in the retina. This causes the eye to be unable to correctly focus on distant objects. In hyperopia (for various reasons) the image focuses on a point farther away than the retina outside the eye. This causes the eye to be unable to focus properly on nearby objects.

I.) For a convergent and divergent lens make the ray diagram for an object at infinity (the rays will be parallel), remember that applies the paraxial approach where the lens is sufficiently fine. Indicate the focal point and explain which lens should be used (and why) to correct each condition.

II.) Using the fine lens equation, which relates the focal point, distance of the object and the image (is the same as that of mirrors) and lens power, analyze the following two cases. Note that the images that are formed with respect to the eye in these cases are always on the same side where the object is located, so they are virtual (for convergent and divergent lenses), this means that the distance of the image is negative.

a.)  A person with myopia has a near point of 12cm and a distant point of 17cm. Calculate the power of the lens necessary so that the person can see very distant objects.

b.) A person with hyperopia has a near point of 100cm. Calculate the power of the lens needed so you can read a paper at a distance of 25cm.

Answer 1

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