Problem 110 - University Physics with Modern Physics

Question

Given that frogs are nearsighted in air, which statement is most likely to be true about their vision in water? (a) They are even more nearsighted; because water has a higher index of refraction than air, a frog's ability to focus light increases in water. (b) They are less nearsighted, because the cornea is less effective at refracting light in water than in air. (c) Their vision is no different, because only structures that are internal to the eye can affect the eye's ability to focus. (d) The images projected on the retina are no longer inverted, because the eye in water functions as a diverging lens rather than a converging lens.

Step-by-Step Solution

Answer

Frogs are less nearsighted in water due to the cornea's reduced effectiveness in refracting light.

Step 1: Understanding the Problem

The problem asks about the vision of frogs when they move from air to water. We need to consider how the refraction of light changes in these different mediums and how it affects frogs' eyesight.

Step 2: Analyzing Refractive Index

Air has a lower refractive index than water. When light travels from air to water, it bends due to the increase in the refractive index. Therefore, the cornea, which significantly refracts light in air, will have a different effect in water.

Step 3: Examining the Cornea's Role

In the air, the cornea contributes majorly to focusing light by bending (refracting) it. However, in water, since water has a similar refractive index to that of the cornea, the cornea becomes less effective at refracting light.

Step 4: Evaluating Options

Based on the analysis, (a) suggests that frogs become more nearsighted because of increased refraction, which is incorrect as the cornea refracts less in water. (b) suggests less nearsightedness due to a less effective cornea, which is logical. (c) suggests vision remains unchanged, ignoring the refractive index's impact. (d) discusses inverted images and diverging lenses, which is unrelated to nearsightedness.

Step 5: Determining the Correct Statement

Given the role of the cornea and changes in refractive indices, option (b) correctly identifies that frogs are less nearsighted in water due to the reduced effectiveness of the cornea in refracting light.

Key Concepts

Refractive Index

The refractive index is a key concept in understanding how light behaves as it moves from one medium to another. It is a measure of how much the speed of light decreases inside a medium compared to a vacuum.
In simpler terms, it indicates how much light bends when entering a new substance.
When light goes from air (with a lower refractive index) into water (with a higher refractive index), it slows down and bends towards the normal.

• Air has a refractive index close to 1.
• Water's refractive index is about 1.33, indicating more bending of light.

This bending or refraction is crucial for vision, as it focuses light rays onto the retina. Changes in the refractive index when moving from air to water greatly impact how animals like frogs see their environment.

Cornea's Role in Vision

The cornea is a transparent layer at the front of the eye that significantly refracts light, especially in air. Its curvature and the difference in refractive indices between air and the cornea allow it to bend light towards the retina.
In air, the cornea's refractive power is significant due to the stark contrast between the refractive indices of air and the corneal tissue. When submerged in water, the contrast in refractive indices between the water and the cornea is reduced. Here's why:

• In air, the cornea's role is amplified due to the large refractive index difference.
• In water, the cornea and the surrounding medium have similar refractive indices, thus weaker refractive power.

This change affects how well the eye can focus light, making the cornea less effective at focusing light when in water.

Light Refraction in Water

Light refraction in water is a critical factor that influences how underwater vision operates. When light travels from a medium like air into water, it refracts, or bends, due to the different refractive indices. This bending is crucial underwater, where the refractive index of water is closer to that of many biological tissues.

• Light slows down as it enters water.
• This reduction in speed causes the light to bend.

The reduced effectiveness of light focus by the cornea in water can lead to clearer vision for aquatic animals who are naturally nearsighted in air.
This happens because the light refracts less upon entering the eye, allowing more of it to focus correctly on the retina.

Nearsightedness in Animals

Nearsightedness, or myopia, occurs when the eyes focus images in front of the retina rather than on it. This makes distant objects appear blurry. In animals, this is often adapted for specific environmental needs. For creatures like frogs, which are nearsighted in air, this is not necessarily a disadvantage. Their lifestyle primarily requires acute up-close vision for hunting and navigating their immediate environment.

• Myopia allows for sharp focus on nearby objects.
• Some animals, like frogs, have adapted eyes for their typical habitats.

When these animals enter water, the effect of nearsightedness can diminish. The decrease in corneal refraction due to water's refractive index often results in clearer distant vision, aligning with underwater needs.