Question

A myopic person's eye has a relaxed focal length of \(1.9 \mathrm{~cm}\). What is the maximum distance from the eye at which she can see an object clearly, and what is the magnification of the lens for an object at this point? A. \(0=1 \mathrm{~cm}, m=-\frac{1}{2}\) B. \(0=38 \mathrm{~cm}, m=-\frac{1}{38}\) C. \(0=38 \mathrm{~cm}, n=-\frac{1}{19}\) D. \(0=50 \mathrm{~cm}, \mathrm{mt}=-\frac{1}{50}\)

Short answer

The maximum object distance is \(1.9 \mathrm{~cm}\), and the magnification is \(-1\). None of the given options match this answer.

Step-by-step solution

Determine the maximum object distance

To find the maximum distance at which the person can see the object clearly, she will need to see it at the farthest point she can focus the light from the object onto her retina. This occurs when the image distance (i) is at its minimum. For a myopic person, this minimum image distance corresponds to the relaxed state of her eye. The relaxed focal length is given by 1.9 cm in this case. Therefore, i = 1.9 cm. Now, let's use the lens formula to find the maximum object distance (o): \(\frac{1}{f} = \frac{1}{o} + \frac{1}{i}\) Substitute f = 1.9 cm and i = 1.9 cm into the formula: \(\frac{1}{1.9} = \frac{1}{o} + \frac{1}{1.9}\)

Solve for the maximum object distance (o)

Simplify the equation and solve for o: \(\frac{1}{o} = \frac{1}{1.9} - \frac{1}{1.9}\) \(\frac{1}{o} = \frac{1}{1.9}\) Flip both sides: o = 1.9 cm So, the maximum object distance at which she can see an object clearly is 1.9 cm.

Calculate the lens magnification (m)

Now we will calculate the magnification using the formula: m = -\(\frac{i}{o}\) Substitute the values for i = 1.9 cm and o = 1.9 cm: m = -\(\frac{1.9}{1.9}\) m = -1 The lens magnification at this point is -1. The maximum object distance is 1.9 cm, and the magnification is -1. Comparing the answer to the available options, we can see that none of them match the correct solution. This means, there might be a typographical error in the given options, or the context of the question might have been incorrectly understood.