How much must an uncorrected 1.00D myope accommodate to image the object which is at a distance of 33.33cm on the retina?
Understand the Problem
The question is asking about the accommodation required for an uncorrected myopic eye with a refractive error of 1.00D to focus on an object at a distance of 33.33cm. We need to calculate the additional power needed for the eye to focus at this distance. The uncorrected myope question requires a single-step formula to solve.
Answer
$2.00 \text{ D}$
Answer for screen readers
$2.00 \text{ D}$
Steps to Solve
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Convert the object distance from cm to meters To use the vergence formula, we need to convert the object distance from centimeters to meters. $33.33 \text{ cm} = 0.3333 \text{ m}$
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Calculate the object vergence (L) Object vergence is the inverse of the object distance in meters.
$L = \frac{1}{d} = \frac{1}{0.3333 \text{ m}} = 3.00 \text{ D}$
- Calculate the accommodation required The uncorrected myope has a refractive error of -1.00 D. This means their eye has 1.00 D too much power for distance. So, we subtract the myopic error from the object vergence to find the accommodation required. Accommodation = Object Vergence - Myopia Accommodation $= 3.00 \text{ D} - 1.00 \text{ D} = 2.00 \text{ D}$
$2.00 \text{ D}$
More Information
The uncorrected myopic eye needs to accommodate 2.00 D to see an object at 33.33 cm clearly.
Tips
A common mistake is forgetting to convert the object distance to meters before calculating the object vergence. Also, some might add the myopic error instead of subtracting, leading to an incorrect result.
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