Physics College

A Nearsighted Eye. A certain very nearsighted person cannot focus on anything farther than 36.0 cm from the eye. Consider the simplified model of the eye. In a simplified model of the human eye, the aqueous and vitreous humors and the lens all have a refractive index of 1.40, and all the refraction occurs at the cornea, whose vertex is 2.60 cm from the retina.

Required:
a. If the radius of curvature of the cornea is 0.65 cm when the eye is focusing on an object 36.0 cm from the cornea vertex and the indexes of refraction are as described before, what is the distance from the cornea vertex to the retina?
b. What does this tell you about the shape of the nearsighted eye?

1. This distance is greater than for the normal eye.
2. This distance is shorter than for the normal eye.

Answers

Answer 1

Answer:

a) The distance from the cornea vertex to the retina is 2.37 cm

b) This distance is shorter than for the normal eye.

Explanation:

a) Let refractive index of air,

n(air) = x = 1

Let refractive index of lens,

n(lens) = y = 1.4

Object distance, s = 36 cm

Radius of curvature, R = 0.65 cm

The distance from the cornea vertex to the retina is the image distance because image is formed in the retina.

Image distance, s' = ?

(x/s) + (y/s') = (y-x)/R

(1/36) + (1.4/s') = (1.4 - 1)/0.65

1.4/s' = 0.62 - 0.028

1.4/s' = 0.592

s' = 1.4/0.592

s' = 2.37 cm

Distance from the cornea vertex to the retina is 2.37 cm

(b) For a normal eye, the distance between the cornea vertex and the retina is 2.60 cm. Since 2.37 < 2.60, this distance is shorter than for normal eye.

Related Questions

A soccer ball is released from rest at the top of a grassy incline. After 2.2 seconds, the ball travels 22 meters. One second later, the ball reaches the bottom of the incline. (Assume that the acceleration was constant.) How long was the incline

Answers

Answer:

x = 46.54m

Explanation:

In order to find the length of the incline you use the following formula:

[tex]x=v_ot+\frac{1}{2}at^2[/tex]      (1)

vo: initial speed of the soccer ball = 0 m/s

t: time

a: acceleration

You first use the the fact that the ball traveled 22 m in 2.2 s. Whit this information you can calculate the acceleration a from the equation (1):

[tex]22m=\frac{1}{2}a(2.2s)^2\\\\a=9.09\frac{m}{s^2}[/tex]      (2)

Next, you calculate the distance traveled by the ball for t = 3.2 s (one second later respect to t = 2.2s). The values of the distance calculated is the lenght of the incline:

[tex]x=\frac{1}{2}(9.09m/s^2)(3.2s)^2=46.54m[/tex]       (3)

The length of the incline is 46.54 m

The smallest shift you can reliably measure on the screen is about 0.2 grid units. This shift corresponds to the precision of positions measured with the best Earth-based optical telescopes. If you cannot measure an angle smaller than this, what is the maximum distance at which a star can be located and still have a measurable parallax

Answers

Answer:

The distance is  [tex]d = 1.5 *10^{15} \ km[/tex]

Explanation:

From the question we are told that

        The smallest shift is [tex]d = 0.2 \ grid \ units[/tex]

Generally a grid unit is  [tex]\frac{1}{10}[/tex] of  an arcsec

  This implies that  0.2 grid unit is  [tex]k = \frac{0.2}{10} = 0.02 \ arc sec[/tex]

The maximum distance at which a star can be located and still have a measurable parallax is mathematically represented as

           [tex]d = \frac{1}{k}[/tex]

substituting values

           [tex]d = \frac{1}{0.02}[/tex]

           [tex]d = 50 \ parsec[/tex]

Note  [tex]1 \ parsec \ \to 3.26 \ light \ year \ \to 3.086*10^{13} \ km[/tex]

So  [tex]d = 50 * 3.08 *10^{13}[/tex]

     [tex]d = 1.5 *10^{15} \ km[/tex]

Other Questions
Can you help me with this question (8x - 4)(7y + 2) multiplying binomials -12.48 -(-2.99)-5.62 ABC has been translated right to create triangle XYZ. Based on this information, which of the following is a true statement? answers: A) B) C) A C D) B X Line j is a straight line. Line j is a straight line. 2 lines come out of the line to form 4 angles. From top left, clockwise, the angles are: x, y, z, w. Which equation represents the relationship between the measures of Angle w and Angle z? Measure of angle w = measure of angle z Measure of angle w + measure of angle z = 90 degrees Measure of angle w + measure of angle z = 100 degrees Measure of angle w + measure of angle z = 180 degrees Ram made his father......(buy)a new bag.(correct form of causive verb) a number between 891 and 909 that is divisible by 10 given that 1=$1..62 what is 650 pounds in dollars After getting their results in, a group of scientists went back and looked at their study. As planned, their experiment consisted of three groups. The first group received a new medicine at a normal dose, the second group received the medicine at half the dose, and the third group received the medicine at twice the dose. Which of the following best describes what went wrong with the scientists study? What problems did the Chinese encounter because of their choice of location, and how did they attempt to solve those problems? Use details.Please help I have been stuck on this question for about an hour. On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below and to the right of the line is shaded. Which linear inequality is represented by the graph? y 2x + 4 y one-halfx + 3 y One-halfx + 3 y 2x + 3 Complete this sentence. The CNS communicates with the body proper through ________. View Available Hint(s) Complete this sentence. The CNS communicates with the body proper through ________. some cranial nerves, some spinal nerves, and some additional nerves that were mentioned but not discussed in the tutorial the spinal nerves but not specifically through the cranial nerves the cranial nerves but not specifically through the spinal nerves some (but not all) of the cranial nerves and some (but not all) of the spinal nerves the cranial nerves and the spinal nerves Write the rectangular equation (x+5) 2 + y 2 = 25 in polar form. A species of spruce tree occupies the same niche at the mouth of a river that a species of pine tree occupies further upstream. One year, several pinecones fall into the river and are carried to the mouth, where they take root and grow amongst the spruce trees. What will be the most likely result of this occurrence The management of a chain of frozen yogurt stores believes that t days after the end of an advertising campaign, the rate at which the volume V (in dollars) of sales is changing is approximated by V ' ( t ) = 26400 e 0.49 t . On the day the advertising campaign ends ( t = 0 ), the sales volume is $ 170 , 000 . Find both V ' ( 6 ) and its integral V ( 6 ) . Round your answers to the nearest cent. A piece of wood near a fire is at 23C. It gains 1,160 joules of heat from the fire and reaches a temperature of 42C. The specific heat capacity ofwood is 1.716 joules/gram degree Celsius. What is the mass of the piece of wood?. 16 gOB. 29 gC. 36 gOD. 61 g Read the excerpt from Part 2 of "The Most Dangerous Game, by Richard Connell. He slid down from the tree, and struck off again into the woods. His face was set and he forced the machinery of his mind to function. Three hundred yards from his hiding place he stopped where a huge dead tree leaned precariously on a smaller, living one. Throwing off his sack of food, Rainsford took his knife from its sheath and began to work with all his energy. The job was finished at last, and he threw himself down behind a fallen log a hundred feet away. He did not have to wait long. In this scene in both the story and the film, Rainsford is depicted as Can someone help me with the below question??? What type of information system would a chain of theaters use to selltickets? What is the area of the triangle below?18