Question 1

The near point of a farsighted person is 65 cm. What power contact lens must he use to correct this problem and be able to read a book at a normal near point of 25 cm?
A) -4.2 diopters
B) -2.5 diopters
C) -2.4 diopters
D) +4.2 diopters
E) +2.5 diopters

Accepted Answer

The answer of The near point of a farsighted person...

Question 2

What is the focal length of the corrective contact lens needed by a nearsighted person whose far point is at 60 cm?
A) -60 cm
B) -30 cm
C) +30 cm
D) +60 cm
E) +130 cm

Accepted Answer

The focal length of the corrective lens for a nearsighted person should allow them to see distant objects clearly. Since their far point is 60 cm, the lens needs to correct vision to infinity. The formula for lens power (P) is P = 1/f, where f is the focal length in meters. To make distant objects (at infinity) appear at the person's far point (60 cm), the lens must have a focal length of -60 cm, indicating a diverging lens. This focal length will shift the image from infinity to the person's far point, correcting their nearsightedness.

Question 3

A myopic (nearsighted) child wears contact lenses that allow her to have clear distant vision. The power of the lenses of her eyeglasses is -3.00 diopters. Without the corrective lenses, what is the far point of the girl?
A) 0.33 m
B) 0.25 m
C) 0.17 m
D) 0.42 m
E) 0.50 m

Accepted Answer

The far point of a myopic person can be calculated using the formula: Far point = 1/Power of the lens in diopters. Therefore, for a lens with a power of -3.00 diopters, the far point = 1/3 = 0.33 meters.

Question 4

A nearsighted person has a far point that is 4.2 m from his eyes. What power contact lenses must he wear to allow him to focus on distant mountains?
A) 0.48 diopters
B) -0.48 diopters
C) -0.36 diopters
D) -0.24 diopters
E) 0.24 diopters

Accepted Answer

The answer of A nearsighted person has a far point...

Question 5

What is the uncorrected near point of a farsighted person who can comfortably read a newspaper held 25 cm from his eyes when he wears +3.33-diopter contact lenses?
A) 1.5 m
B) 0.50 m
C) 1.9 m
D) 0.75 m
E) 0.60 m

Accepted Answer

The answer of What is the uncorrected near point of...

Question 6

A farsighted girl has a near point at 2.0 m but has forgotten her glasses at home. The girl borrows eyeglasses that have a power of +2.75 diopters. With these eyeglasses, what is the near point of the girl, assuming that she wears them extremely close to her eyes?
A) 28 cm
B) 31 cm
C) 33 cm
D) 37 cm
E) 40 cm

Accepted Answer

The answer of A farsighted girl has a near point...

Question 7

A person's hyperopic (farsighted) eye can focus on objects that are 75 cm away and farther. What power and what focal length contact lenses should be prescribed so this person can see objects 25 cm and farther from the eye?

Accepted Answer

The answer of A person's hyperopic (farsighted) eye can focus...

Question 8

A nearsighted man wears contact lenses of -3.00 diopters. With these lenses, his corrected near point is 25.0 cm. What is his uncorrected near point?

Accepted Answer

The answer of A nearsighted man wears contact lenses of...

Question 9

As a treatment for cataracts (a cloudiness of the lens of the eye), the natural lens is removed and a plastic lens is implanted. After this is done a person can see distant objects clearly, but he cannot accommodate to focus on nearby objects. If such a person wanted to read a book at a distance of 25 cm, he would have to wear contact lenses having a diopter power of
A) +2.78 diopters
B) +3.33 diopters
C) -1.78 diopters
D) +4.00 diopters
E) -4.00 diopters

Accepted Answer

The answer of As a treatment for cataracts (a cloudiness...

Question 10

What power contact lens should be used to correct the vision of a farsighted person whose near point is 80 cm so she can see things clearly that are 25 cm in front of her?
A) +2.8 diopters
B) -2.8 diopters
C) -4.0 diopters
D) -4.2 diopters
E) +4.2 diopters

Accepted Answer

The answer of What power contact lens should be used...

Question 11

A nearsighted person has a far point that is 4.2 m from his eyes. What focal length lenses must he use in his contact lenses to allow him to focus on very distant mountains?
A) -4.2 m
B) 4.2 m
C) -5.2 m
D) 5.2 m
E) -4.8 m

Accepted Answer

The correct focal length for the lenses is -4.2 m. This is because a nearsighted person needs diverging lenses to correct their vision, which have a negative focal length. The far point distance indicates the maximum distance at which the person can see clearly without correction. To see distant objects clearly, the lenses must have a focal length that effectively extends this far point to infinity, which is achieved with a focal length that matches the negative of the far point distance.

Question 12

A machinist with normal vision has a near point at 25 cm. This machinist wears +4.25-diopter eyeglasses in order to do very close work. With these eyeglasses, what is the near point of the machinist? Assume that he wears the glasses extremely close to his eyes.
A) 12 cm
B) 10 cm
C) 7 cm
D) 15 cm
E) 17 cm

Accepted Answer

The near point with eyeglasses can be calculated using the lens formula: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the image distance (in this case, the new near point), and u is the object distance (the original near point). For a +4.25 diopter lens, f = 1/D = 1/4.25 m = 0.235 m (or 23.5 cm). Since the glasses are worn very close to the eyes, we can assume the image is formed at the near point of the eyes without the glasses, which is 25 cm. Substituting these values into the lens formula gives us the new near point closer than the original 25 cm, specifically at 12 cm.

Question 13

What power contact lens must be used to correct the vision of a nearsighted person whose far point is 40 cm?
A) +2.5 diopters
B) -2.5 diopters
C) -3.6 diopters
D) -4.0 diopters
E) +4.0 diopters

Accepted Answer

The power of a lens required to correct nearsightedness is negative. The formula for calculating the power of a lens is P = 1/f where P is the power in diopters and f is the focal length in meters. The far point of a nearsighted person is the distance beyond which they cannot see clearly. For a nearsighted person with a far point of 40 cm, their focal length is -40 cm or -0.4 m. Therefore, P = 1/(-0.4) = -2.5 diopters. Thus, the correct power contact lens for this person would be -2.5 diopters.

Question 14

Without glasses, a person can comfortably read a magazine when it is held at 60 cm from his eyes. What should be the focal length of his contact lenses to allow him to read the magazine comfortably at a distance of 30 cm?
A) -30 cm
B) +30 cm
C) -60 cm
D) +60 cm
E) +90 cm

Accepted Answer

From the given problem, we can use the lens formula:

1/f = 1/v - 1/u

where f is the focal length of the lens, u is the object distance (60 cm when reading comfortably without glasses), and v is the image distance (30 cm when reading comfortably with the contact lenses).

Plugging in the values, we get:

1/f = 1/30 - 1/60

Simplifying this equation, we get:

1/f = 1/60

Therefore, f = +60 cm, which means the person needs contact lenses with a focal length of +60 cm to read comfortably at a distance of 30 cm. The positive sign indicates that the contact lenses should be converging, which is the most common type of contact lens used for correcting nearsightedness.

Question 15

What is the power of the lens that has a focal length of 40 cm and a diameter if 5.0 cm?
A) -2.5 diopters
B) +20 diopters
C) +0.20 diopters
D) +2.5 diopters
E) +2.7 diopters

Accepted Answer

Using the formula for power of a lens (P = 1/f), where f is the focal length in meters, we get P = 1/0.4 = +2.5 diopters.

Question 16

A farsighted boy has a near point at 2.3 m and requires contact lenses to correct his vision to the normal near point. What is the correct choice of lens power for the contact lenses?
A) -0.28 diopters
B) +0.28 diopters
C) -3.6 diopters
D) +3.6 diopters
E) +1.8 diopters

Accepted Answer

The lens power required to correct farsightedness is positive. 
The lens power required can be found using the formula: 
Lens power (in diopters) = 1/focal length (in meters)

Given, near point distance = 2.3 m (which is the far point for the farsighted boy)
So, focal length = 1/2.3 m = 0.43 m

To correct the vision to the normal near point, we need to bring the near point to 25 cm (0.25 m) 
So, the new focal length required = 0.25 m

Lens power required = 1/0.25 m - 1/0.43 m = 4 - 2.32 = 1.68 
Therefore, the correct choice of lens power for the contact lenses is +1.68 diopters, which is closest to option D, +3.6 diopters.

Question 17

What is the power of a lens that has a focal length of -40 cm and a width of 2.0 cm?
A) -2.5 diopters
B) -0.50 diopters
C) +4.0 diopters
D) +2.5 diopters
E) -50 diopters

Accepted Answer

The power of a lens with focal length f (in meters) is given by:
P = 1/f
We are given the focal length in cm, so we need to convert it to meters:
f = -40 cm = -0.4 m
Now we can calculate the power:
P = 1/(-0.4 m) = -2.5 diopters.

Question 18

A nearsighted person has a far point of 50 cm for his right eye and 150 cm for his left eye. For each eye, what power contact lens will allow the person to see gorgeous sunsets?

Accepted Answer

The answer of A nearsighted person has a far point...

Question 19

What is the focal length of a contact lens that will allow a person with a near point of 125 cm to read a physics book held 25.0 cm from his eyes?
A) -100 cm
B) -31.3 cm
C) 10.2 cm
D) 20.8 cm
E) 31.3 cm

Accepted Answer

We can use the lens equation:

1/f = 1/d_o + 1/d_i

where f is the focal length of the contact lens, d_o is the distance from the lens to the object (the book) and d_i is the distance from the lens to the image (the retina).

We know that the near point (the closest distance at which the person can focus) is 125 cm, so that means d_i = -125 cm (negative because the image is virtual, on the same side of the lens as the object).

We also know that the person holds the book 25 cm from his eyes, so d_o = 25 cm.

Substituting these values into the lens equation gives:

1/f = 1/25 cm - 1/125 cm

Simplifying:

1/f = (5 - 1)/125 cm = 4/125 cm

f = 31.25 cm

So the focal length of the contact lens that would allow the person to read the book is 31.3 cm, which is closest to choice (E).

Question 20

The power of a lens is 4.0 diopters and its diameter is 5.0 cm. What is the focal length of this lens?
A) 25 cm
B) 55 cm
C) 10 cm
D) 0.25 cm
E) 2.5 cm

Accepted Answer

The formula to find the focal length of a lens in meters is given by:
f = 1/diopter = 1/4 = 0.25 m
We need to convert the diameter of the lens from cm to m:
d = 5.0 cm = 0.05 m
Now, we can use the formula for the area of a circle:
A = πr^2
where r is the radius (half of the diameter) of the lens. Solving for r, we get:
r = √(A/π) = √(0.0019635/π) = 0.025 m
Finally, we can use the formula for the focal length of a thin lens:
1/f = (n-1)(1/r1 - 1/r2)
where n is the refractive index of the lens (assumed to be 1.5 for simplicity), and r1 and r2 are the radii of curvature of the two surfaces of the lens. Since the lens is assumed to be thin, we can assume that both radii are equal to the radius of the lens (r1 = r2 = r). Substituting the values, we get:
1/0.25 = (1.5-1)(1/r - 1/r) = 0
Therefore, the focal length of the lens is f = 25 cm.

Quiz 19: Optical Instruments

The near point of a farsighted person is 65 cm. What power contact lens must he use to correct this problem and be able to read a book at a normal near point of 25 cm?

What is the focal length of the corrective contact lens needed by a nearsighted person whose far point is at 60 cm?

A myopic (nearsighted) child wears contact lenses that allow her to have clear distant vision. The power of the lenses of her eyeglasses is -3.00 diopters. Without the corrective lenses, what is the far point of the girl?

A nearsighted person has a far point that is 4.2 m from his eyes. What power contact lenses must he wear to allow him to focus on distant mountains?

What is the uncorrected near point of a farsighted person who can comfortably read a newspaper held 25 cm from his eyes when he wears +3.33-diopter contact lenses?

A farsighted girl has a near point at 2.0 m but has forgotten her glasses at home. The girl borrows eyeglasses that have a power of +2.75 diopters. With these eyeglasses, what is the near point of the girl, assuming that she wears them extremely close to her eyes?

A person's hyperopic (farsighted) eye can focus on objects that are 75 cm away and farther. What power and what focal length contact lenses should be prescribed so this person can see objects 25 cm and farther from the eye?

A nearsighted man wears contact lenses of -3.00 diopters. With these lenses, his corrected near point is 25.0 cm. What is his uncorrected near point?

What power contact lens should be used to correct the vision of a farsighted person whose near point is 80 cm so she can see things clearly that are 25 cm in front of her?

A nearsighted person has a far point that is 4.2 m from his eyes. What focal length lenses must he use in his contact lenses to allow him to focus on very distant mountains?

A machinist with normal vision has a near point at 25 cm. This machinist wears +4.25-diopter eyeglasses in order to do very close work. With these eyeglasses, what is the near point of the machinist? Assume that he wears the glasses extremely close to his eyes.

What power contact lens must be used to correct the vision of a nearsighted person whose far point is 40 cm?

Without glasses, a person can comfortably read a magazine when it is held at 60 cm from his eyes. What should be the focal length of his contact lenses to allow him to read the magazine comfortably at a distance of 30 cm?

What is the power of the lens that has a focal length of 40 cm and a diameter if 5.0 cm?

A farsighted boy has a near point at 2.3 m and requires contact lenses to correct his vision to the normal near point. What is the correct choice of lens power for the contact lenses?

What is the power of a lens that has a focal length of -40 cm and a width of 2.0 cm?

A nearsighted person has a far point of 50 cm for his right eye and 150 cm for his left eye. For each eye, what power contact lens will allow the person to see gorgeous sunsets?

What is the focal length of a contact lens that will allow a person with a near point of 125 cm to read a physics book held 25.0 cm from his eyes?

The power of a lens is 4.0 diopters and its diameter is 5.0 cm. What is the focal length of this lens?