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SERCPTT L$..$P$.$USY.IVII.

A person decides to use an old pair of eyeglasses to make some optical instruments. He knows that the near point in his left eye is $54\mathrm{.}0$ cm and the near point in his right eye is $116$ cm $.$

$($a$)$ What is the maximum angular magnification he can produce in a telescope?

$q,$ Determine the focal length that each eyeglass lens must have in order to correct the user's vision by forming an image that when used as the object for the eye's own lens, forms a sharp image on the retina. Then use the calculated focal lengths to find the maximum magnification that a telescope made of the two lenses could have.

$($b$)$ If he places the lenses $10\mathrm{.}0$ cm apart, what is the maximum overall magnification he can produce in a microscope? Hint: Go back to basics and use the thin$-$lens equation to solve part $($b$).$

Consider at what distance from the eye the eyepiece must form its image to be viewed comfortably. Then using the focal lengths calculated in part $($a$)$ for each lens arrangement, calculate the magnification and location of the image formed by the eyeplece. Then use that image as the object for the second lens in order to find its image location and magnification.