Question

1. Stephanie is nearsighted. The farthest object that she can see clearly without using corrective lenses (glasses or contact lenses) is 114 cm away. If she wishes to clearly see an object that is located at infinity (the normal Far Point), she will need to use glasses. What focal length (in cm) will she need for the lenses in her glasses in order to see an object that is located at infinity? Pay attention to the sign conventions for lenses. Make sure that you review the Ray Diagram that shows what happens when a nearsighted eye views a distant object. Do you remember what the basic refraction error is for a nearsighted eye?
What is the Lens Power (in m-1) for this lens?

2. Light from an object enters your eye, is refracted by the lens system (cornea and lens), and an image is formed at the back wall of your eye. This is how we see! Suppose that the distance from the lens system (cornea and lens) to the back wall of your eye is 2.3 cm. If an object is located at 25 cm (the normal Near Point for a healthy eye), what focal length (in cm) is required for the lens system (cornea and lens) in order to create a sharply focused image on the retina? You must keep at least 3 significant digits in your answer. If an object is located at infinity (the normal Far Point for a healthy eye), what focal length (in cm) is required for the lens system (cornea and lens) in order to create a sharply focused image on the retina? During "accommodation", what is the range (in cm) of focal lengths that the lens system (cornea and lens) must have in order to see objects that are located at distances from 25 cm to infinity? In other words, by how many centimeters does the focal length of the eye have to change in order for us to clearly see both nearby and distant objects? You must keep at least 3 significant digits in your answer.

Answer 1

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1) In case of a nearsighted person, an object at infinity comes to a focus in front of the retina. A diverging lens in front of the eye can be used to correct this.  The concave lens focuses light from an object beyond the far point to produce an image that is at the far point.

As the question said that the person need to use glasses. Note that it MATTERS whether a person uses contact lens or glasses. As contact lens sits on the eye, we don't need to worry about any thing but in case of glasses which are usually worn 2 cm in front of the eye, the focal length will decrease by 2 cm

First,

let's assume that a contact lens is to be prescribed.

using lens equation

1/f = 1/do + 1/di

where do is object distance and di is image distance

here, do is infinity,

so,

1/f = 1/di

1/f = 1/114

f = - 114 cm ( negative sign indicates diverging lens)

therefore, a contact lens with focal length of - 114 cm or - 1.14 m is needed

Power = 1 / f

Power = - 1 / 1.14

Power = - 0.877 D

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If we consider glasses, then

f = - 114 + 2 = -112 cm or - 1.12 m

then

P = - 0.893 D