Question

Joe is hiking through the woods when he decides to stop and take in the view. He is particularly interested in three objects: a squirrel sitting on a rock next to him, a tree a few meters away, and a distant mountain. As Joe is taking in the view, he thinks back to what he learned in his physics class about how the human eye works.

Light enters the eye at the curved front surface of the cornea, passes through the lens, and then strikes the retina and fovea on the back of the eye. The cornea and lens together form a compond lens system. The large difference between the index of refraction of air and that of the aqueous humor behind the cornea is responsible for most of the bending of the light rays that enter the eye, but it is the lens that allows our eyes to focus. The ciliary muscles surrounding the lens can be expanded and contracted to change the curvature of the lens, which in turn changes the effective focal length of the cornea-lens system. This in turn changes the location of the image of any object in one's field of view. Images formed on the fovea appear in focus. Images formed between the lens and the fovea appear blurry, as do images formed behind the fovea. Therefore, to focus on some object, you adjust your ciliary muscles until the image of that object is located on the fovea.
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A.) Joe first focuses his attention (and his eyes) on the tree. The focal length of the cornea-lens system in his eye must be __________ the distance between the front and back of his eye.

greater than
less than
equal to

Less than is the correct answer

B.) Joe's eyes are focused on the tree, so the squirrel and the mountain appear out of focus. This is because the image of the squirrel is formed ______ and the image of the mountain is formed _____.

between the lens and fovea / between the lens and fovea
between the lens and fovea / behind the fovea
behind the fovea / between the lens and fovea
behind the fovea / behind the fovea

The correct answer is behind the fovea/between the lens and fovea.

C.) Joe now shifts his focus from the tree to the squirrel. To do this, the ciliary muscles in his eyes must have _____ the curvature of the lens, resulting in a(n) _______ focal length for the cornea-lens system. Note that curvature is different from radius of curvature.

increased / increased
increased / decreased
decreased / increased
decreased / decreased

I don't know how to get this answer. Please help!

Answer 1

Concepts and reason

The required concepts to solve this question are focal length, radius of curvature and ciliary muscles function in eyes.

First use the image and object distance to compare the focal length of the cornea lens system. Later use the focal length and compare whether the rays converge to fovea. Finally use the object distance to compare the radius of curvature and focal length of the eye lens.

Fundamentals

Ciliary muscles help to change the shape of the lens which changes the focal length of the eye lens. Ciliary muscles change the curvature according to the distance of the object to be focused. The ciliary muscles surrounding the lens can be expanded and contracted to change the curvature of the lens, which in turn changes the effective focal length of the cornea-lens system. The image is formed on the fovea.

When the ciliary muscles contract, the radius of curvature increases and focal length decreases.

When ciliary muscles relax then curvature decreases and focal length increases.

Focal length is the point at which all the ray converges to meet after passing through a diverging lens.

The radius of curvature of lens is twice the focal length distance and center of the circle formed by the lens curvature.

(A)

Light come into the eye at the curled front surface of the cornea, permits over the lens, and then strikes the fovea and retina on the back of the eye. The lens and cornea form a compound lens system. Cornea is outermost lens of the eye.

Hence, the correct answer is less than the distance between the front and back of his eye.

(B)

When the object is too near then image formed by lens is behind the retina. Squirrel is close to joe eyes so image formed behind the retina or fovea. If the object is far away, then image formed by lens is in front of the retina. Mountain are far away from the joe eyes so image formed between lens and retina.

When joe eyes are focused on the tree, that time the squirrel and the mountain appear out of focus. This is because the image of the squirrel is formed behind the fovea and the image of the mountain is formed between lens and fovea.

(C)

When the object is at far away ciliary muscles relax decreasing the curvature of the lens resulting increase in the focal length. When object is close ciliary muscles contract, increasing the curvature of the lens and decreasing the focal length.

When joe eyes are focused on the squirrel. The ciliary muscles of joe eyes must have increased the curvature of the lens, resulting in decreased focal length for the cornea-lens system.

Ans: Part A

The correct answer is less than.