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Question Video: Understanding How Convex Lenses Can Correct Farsightedness Science

The figure shows a farsighted eye. If lens A is placed in front of the eye, does the light focus nearer to or farther from the retina of the eye?

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Video Transcript

The following figure shows a farsighted eye. If lens A is placed in front of the eye, does the light focus nearer to or farther from the retina of the eye?

In this question, we see two light rays that are diverging from a point. We can also see an eye. The question states that the eye is farsighted. We can see that the light rays enter the farsighted eye and these rays cross paths at a point behind the back of the eye. Finally, the question shows a convex lens, lens A, and concave lens, lens B, and asks whether placing lens A in front of the eye would make the light entering the eye focus nearer to or farther from the retina of the eye.

Let us think about what is meant by focusing. Light rays are focused if they converge at a point, called the focal point. The distance from a lens to its focal point is called its focal length. We can see that the two light rays do converge to a point, the point behind the back of the eye.

Let us think about what is meant by retina. The retina of an eye is part of the eye that light must be focused on for the eye to see correctly. The retina is located at the back of the eye. We can see that the eye in the question does not focus the light rays shown at the retina of the eye.

Let us think about what is meant by farsighted. An eye is farsighted if it can correctly focus only light from faraway objects. A farsighted eye cannot correctly focus light from nearby objects. In the question, the two light rays diverge from a point. The point from which the light rays diverge is the position of an object. The less the distance between the object and the eye, the greater the divergence of the light rays from the object that enter the eye.

So we see that the question shows an eye failing to correctly focus light rays diverging from a nearby object, specifically focusing these light rays behind the retina rather than at the retina. It is important to understand that the initially diverging light rays eventually being focused must mean that when the light rays enter the eye, the rays change direction so that they converge rather than diverge after they enter the eye.

We can see then that the fact that the light rays focus behind the retina means that the eye changed the direction of the light rays by too small an angle to make the rays converge at the retina. If the angle that the light rays change direction by was greater, the light rays could converge at the retina. Another way of describing this is that if the focal length for the eye was decreased, these light rays could converge at the retina.

The question is asking whether passing through lens A before entering the eye would change the paths of the light rays that enter the eye so that they focus closer to the retina or farther from the retina. To decide whether lens A can produce this result, we need to understand the effect of lens A on the paths of the diverging light rays from the object.

Recall that lens A is a convex lens. This is because a convex lens will cause incident parallel light rays to converge after they exit the lens. Parallel light rays neither diverge nor converge. Causing parallel rays to converge is the opposite of causing the rays to diverge. We can see then that a convex lens can be considered antidivergent, in that it does the opposite of increasing the divergence of light rays. If we think of a convex lens as reducing the divergence of light rays, we can deduce that if divergent light rays enter a convex lens, the rays will diverge less after they exit the lens.

Recall that the farsighted eye could not focus the incident diverging light rays of the retina, as the eye did not change the directions of the light rays enough. The light rays were changed from diverging to converging, but the eye had too great a focal length to focus these rays at the retina. If the light rays that enter the eye are made to be less divergent by the correct amount before they enter the eye, then the focal length of the eye would be sufficient to focus the rays at the retina.

We know that as lens A is convex, it will reduce the divergence of the light rays from the object. Therefore, placing lens A in front of the eye could change the path of light rays so that they converged at the retina. Even if lens A did not exactly focus these rays at the retina, the rays would be focused nearer to the retina than if lens A was not used. We conclude that placing lens A in front of the eye will focus the light rays from the object nearer to the retina.

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