Optics with corrective eyeglasses

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To correct Uncle Albert's myopia, the required eyeglass lens power is -4.45 diopters (D). The calculation involves using the lens formula, where the object distance (do) is between 24.2 cm and 185 cm, and the lens sits 1.66 cm from the eyes. The process includes finding the focal length (f) using the formula 1/do + 1/di = 1/f, leading to a focal length of approximately 90.68 cm. The final calculation confirms that the lens power needed is -4.45 D, indicating a diverging lens is necessary for correction. Understanding these calculations is crucial for effectively addressing myopia with corrective lenses.
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Homework Statement


Without glasses, your uncle Albert can see things clearly only if they are between 24.2 cm and 185 cm from his eyes. What power eyeglass lens will correct your uncle's myopia? Assume the lenses will sit 1.66 cm from his eyes.


Homework Equations



1/do + 1/di = 1/f

The Attempt at a Solution



I got the answer right but I'm not sure why it was right. If someone can explain this for me, it would be greatly appreciated. Thanks.
 
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Answer: -4.45 diopters (D) 1/24.2 + 1/185 = 1/f 1/f = 0.010978836 f = 90.6834 1/90.6834 + 1/d = 1/1.66 1/d = 4.45 d = -4.45 D
 
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