Question

When a diver with \(20 / 20\) vision removes her mask underwater, her vision becomes blurry. Why is this the case? Does the diver become nearsighted (eye lens focuses in front of retina) or farsighted (eye lens focuses behind retina)? As the index of refraction of the medium approaches that of the lens, where does the object get imaged? Typically, the index of refraction for water is 1.33 , while the index of refraction for the lens in a human eye is \(1.40 .\)

Short answer

Answer: When a diver removes their mask underwater, their vision becomes nearsighted (myopic) because the light converges less when it passes through water, which has a different index of refraction than air. This results in the lens focusing light in front of the retina.

Step-by-step solution

Understand the Principle of Refraction and its Effect on Vision

Refraction is a phenomenon in which light changes direction when it passes from one medium to another, with differing indices of refraction. This change in direction causes the light to bend, which can impact how the lens in the eye focuses the incoming light on the retina. In the case of the diver, the refraction of light is altered due to the change in medium as the light passes through the water and enters the eye.

Determine Whether the Diver's Vision Becomes Nearsighted or Farsighted

When wearing the mask, there is a layer of air between the diver's eye and the water. This allows the eye to focus properly on objects underwater. When the mask is removed, the eye is directly in contact with water, which has a different index of refraction than air. The diver's eye lens must now adjust to focus on objects in the water, with its index of refraction 1.33. Comparing the index of refraction of water which is 1.33 to the human eye's lens index of refraction, which is 1.40, the light converges less when it passes through water than through air. This results in the lens focusing light in front of the retina, making the diver myopic, or nearsighted.

Discuss Image Formation as the Index of Refraction of the Medium Approaches that of the Lens

As the index of refraction of the surrounding medium (water) approaches that of the lens (1.40), the light bending at the lens's interface decreases. As a result, the power of the lens to focus light decreases, causing the image to be formed at a greater distance from the lens. When the index of refraction of water becomes equal to that of the lens, the lens will lose its ability to focus the light, and the object will be imaged at infinity, making it impossible to focus on nearby objects.

Key concepts

Nearsightedness and Farsightedness

Nearsightedness, also known as myopia, occurs when the light entering the eye is focused in front of the retina instead of on it. This means that nearby objects may be seen clearly, but distant objects are blurred.
In contrast, farsightedness, or hyperopia, occurs when light is focused behind the retina. People with farsightedness often see distant objects more clearly than close ones.

For a diver with 20/20 vision, removing the mask underwater leads to a change in the index of refraction that affects how light is focused. Without the air pocket from the mask, the diver's eyes directly interface with the water, altering the way they focus light. This results in nearsightedness because the change in medium causes light to focus in front of the retina.

Index of Refraction

The index of refraction is a measure of how much light bends when it enters a different medium. This is dependent on the speed of light in those mediums.
A higher index of refraction indicates that light travels slower in that medium. For example, the index of refraction for air is approximately 1.00, while water has an index of 1.33, and the human eye's lens is about 1.40.

When a diver removes their mask underwater, the index of refraction between the eye's lens and the water becomes more similar, which reduces the bending effect at the lens. This reduction in refraction alters the focal point of light entering the eye, leading to blurry vision.

Optical Physics

Optical physics is a branch of science that studies the behavior of light and its interactions with matter. This includes phenomena such as reflection, refraction, and absorption.
When considering a diver's vision underwater, optical physics explains how light interacts at the boundary between water and the eye, leading to an altered focusing effect.

Understanding these principles helps us comprehend why myopia occurs when the mask is removed. The refraction changes because of the similar refractive indices of water and the eye's lens, leading to changes in how light is focused and hence, impacting vision clarity.

Light Behavior in Different Mediums

When light travels from one medium to another, its speed and direction change, a process known as refraction. The degree to which light bends depends on the indices of refraction of the two media.
In the scenario of a diver, light passes from water into the eye, a transition with only a small difference in refractive indices. This leads to a much less pronounced bending of the light rays compared to the air-water interface usually present when wearing a mask.

As the refractive index of water (1.33) is closer to that of the eye lens (1.40), the reduction in refraction makes focusing more challenging, causing the diver to become nearsighted. This is a practical demonstration of how light behaves differently across various mediums and affects vision.