Chapter 26: Q19PE (page 956)

Repeat the previous problem for glasses that are 1.75 cm from the eyes.

Expert verified

The far point for glasses that are 1.75 cm from the eyes is 26.8 cm.

Step by step solution

Myopia is a vision condition in which visual pictures focus in front of the retina of the eye, creating vision problems of distant objects.

$d_{i} = 1.75 c m (\frac{1 m}{100 c m}) = 0.0175 m$

The power needed (P) to correct the vision can be obtained using the expression,

$P = \frac{1}{d_{0}} + \frac{1}{d_{i}}$

The power of the lens is equal to the reciprocal of the focal length. therefore,

$P = \frac{1}{f} P = \frac{1}{d_{0}} + \frac{1}{d_{i}}$

Rearrange and solve for the image's distance from the eye, we will get

$d_{i} = \frac{1}{P - \frac{1}{\infty}} = \frac{1}{- 4 D - \frac{1}{\infty}} d_{i} = - 0.25 m$

Hence, for the glasses that are 1.75 cm from the eyes, the distance between the eye and the image will be - 0.25 m - 0.0175 m = 0.268 m or 26.8 cm

Therefore, the far point for glasses that are 1.75 cm from the eyes is 26.8 cm

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