Question 1

The objective lens of a refracting telescope has a focal length of 60 cm and the eyepiece a focal length of 8.0 cm. What is the angular magnification of the telescope?
A)34
B)480
C)68
D)0
E)7.5

Accepted Answer

The angular magnification of a telescope is given by the formula: M = F_objective / F_eyepiece. Substituting the given values, M = 60 cm / 8.0 cm = 7.5.

Question 2

What is the maximum possible magnification of the converging lens of focal length 5 cm?
A)2
B)3
C)4
D)5
E)6

Accepted Answer

The answer of What is the maximum possible magnification of...

Question 3

A person can read the newspaper when it is held at 60 cm from his eyes. What should the focal length of his contact lenses be to allow him to read the newspaper comfortably at a distance of 30 cm?
A)-30 cm
B)+30 cm
C)-60 cm
D)+60 cm
E)+90 cm

Accepted Answer

The equation for calculating the focal length of a lens is:

1/f = 1/o + 1/i

where f is the focal length, o is the distance of the object from the lens, and i is the distance of the image from the lens.

In this case, the person can read the newspaper when it is held at a distance of 60 cm, which is the distance of the object from the lens. We want to find the focal length of the lens that will allow the person to read the newspaper comfortably at a distance of 30 cm, which is the distance of the image from the lens.

So, we can use the equation:

1/f = 1/o + 1/i

1/f = 1/60 + 1/30

1/f = 1/20

f = 20 cm

Therefore, the focal length of the contact lenses should be +20 cm, which means they are converging lenses. The correct answer is D.

Question 4

What is the focal length of a pair of contact lenses that will allow a person with a near point of 125.0 cm to read a newspaper 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

The answer of What is the focal length of a...

Question 5

Jill is farsighted and cannot see objects clearly that are closer to the eye than 80.0 cm. What is the focal length of the contact lenses that will enable her to see objects at a distance of 25.0 cm from her eyes?
A)+36.4 cm
B)-36.4 cm
C)-21.2 cm
D)+21.2 cm
E)+32.5 cm

Accepted Answer

The answer of Jill is farsighted and cannot see objects...

Question 6

What is the magnification of a magnifying glass of focal length 4.0 cm if the image is to be viewed by a relaxed eye with a near point of 25 cm?
A)2.0
B)3.0
C)3.6
D)4.0
E)6.3

Accepted Answer

The answer of What is the magnification of a magnifying...

Question 7

Jill is farsighted and cannot see objects clearly that are closer to the eye than 80.0 cm. What is the refractive power of the contact lenses that will enable her to see objects at a distance of 25.0 cm from her eyes?
A)+2.75 diopters
B)-2.75 diopters
C)-4.72 diopters
D)+4.72 diopters
E)+7.00 diopters

Accepted Answer

The answer of Jill is farsighted and cannot see objects...

Question 8

A nearsighted person has her distant vision corrected using a -2.0 D lens. Her uncorrected near point is 15 cm. What is her near point using this lens if the lens is 2.0 cm from the eye?
A)17 cm
B)20 cm
C)13 cm
D)18 cm
E)15 cm

Accepted Answer

The answer of A nearsighted person has her distant vision...

Question 9

What power contact lens should be used to correct the vision of a farsighted person whose near point is 80 cm to see something clearly at a distance of 25 cm?
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 10

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

A nearsighted person has difficulty seeing objects far away. The far point, which is the farthest distance that a person can see objects clearly, is less than infinity. In this case, the far point is 40 cm. To correct this vision, a negative lens must be used, with a power equal to the reciprocal of the far point in meters. 40 cm converted to meters is 0.4 m, so the power of the lens would be -1/0.4 = -2.5 diopters. Therefore, the correct answer is B.

Question 11

John is nearsighted and cannot see things beyond 90 cm from his eyes. What is the refractive power of the contact lenses that will enable him to see distant objects clearly?
A)+1.1 diopters
B)-1.1 diopters
C)-1.7 diopters
D)-2.2 diopters
E)+2.2 diopters

Accepted Answer

The answer of John is nearsighted and cannot see things...

Question 12

A far sighted person can not see clearly objects that are closer to his eyes than 60.0 cm. Which one of the following combinations represents the correct focal length and the refractive power of the contact lenses that will enable him to see the objects at a distance of 25.0 cm from his eyes?
A)-42.9 cm, +2.33 diopters
B)-42.9 cm, -2.33 diopters
C)+42.9 cm, +2.33 diopters
D)+42.9 cm, -2.33 diopters
E)+60 cm, +42.9 diopters

Accepted Answer

To enable a far sighted person to see objects at 25.0 cm, the lenses need to converge the light rays entering the eyes. This means the contact lenses should have a positive refractive power. Also, since the person cannot see objects closer than 60.0 cm, the focal length of the lenses should be less than 60.0 cm. 
Using the lens equation: 
1/f = 1/do + 1/di 
Where f is the focal length, do is the object distance, and di is the image distance. We can rearrange the equation to solve for f: 
1/f = (di - do) / (di x do) 
Assuming that the object distance is -25.0 cm (since the object is closer than the far point of 60.0 cm), and the image distance should be -f (since the lenses are creating a virtual image), we can substitute into the equation and solve for f: 
1/f = (-f - (-25.0)) / (-f x (-25.0)) 
Simplifying, 
1/f = (1/f + 1/25) / f 
1 = (1/f^2) + (1/25f) 
25f = f^2 + 25 
Rearranging and solving the quadratic equation: 
f^2 - 25f + 25 = 0 
f = 42.9 cm 
Since the lenses have a positive refractive power, we can use the equation: 
P = 1/f in diopters to solve for the refractive power: 
P = 1/0.429 = 2.33 diopters 
Therefore, the correct choice is C.

Question 13

A magnifying glass produces an angular magnification of 7. What is the focal length of this lens if a person whose near point is 28 cm reads a book using this magnifying glass?
A)2 cm
B)3 cm
C)4 cm
D)5 cm
E)6 cm

Accepted Answer

The formula for angular magnification is: 
m = -v/u, where v is the distance between the lens and the image, and u is the distance between the lens and the object. 
We know that m = 7, and the person's near point is 28 cm. This means that the object is at a distance of u = 28 cm from the lens. 
We can rearrange the formula to solve for the focal length: 
m = -v/u 
7 = -v/28 
v = -196 cm 
Since the magnifying glass is a converging lens, the focal length is positive. 
Using the lens formula 1/f = 1/v - 1/u, we can solve for f: 
1/f = 1/196 - 1/28 
1/f = (28 - 196)/(196*28) 
1/f = -1/784 
f = -784 cm 
Again, since the lens is converging, the focal length should be positive. Therefore, 
f = 784 cm = 7.84 cm 
Therefore, the focal length of the lens is 7.84 cm, which is closest to choice C (4 cm).

Question 14

A nearsighted person has a far point that is 4.2 m from his eyes. What focal length lenses in diopters he must use in his contacts to allow him to focus on distant objects?
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 15

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 distant objects?
A)-4.2 m
B)4.2 m
C)-5.2 m
D)5.2 m
E)4.8 m

Accepted Answer

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

Question 16

What is the near point of a farsighted person who can read a newspaper held 25 cm from his eyes when he wears 3.33 diopters glasses?
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 near point of a...

Question 17

John is nearsighted and cannot see things beyond 110 cm from his eyes. What is the focal length of the contact lenses that will enable him to see distant objects clearly?
A)+50 cm
B)-50 cm
C)-110 cm
D)+110 cm
E)-30 cm

Accepted Answer

The answer of John is nearsighted and cannot see things...

Question 18

A magnifying glass uses a converging lens with a refractive power of 20 diopters. What is the magnification if the image is to be viewed by a relaxed eye with a near point of 25 cm?
A)5.0
B)3.0
C)4.0
D)1.0
E)2.0

Accepted Answer

The answer of A magnifying glass uses a converging lens...

Question 19

A nearsighted person cannot see objects beyond 80 cm from his eyes. Which one of the following combinations represents the correct focal length and the refractive power of the contact lenses that will enable him to see the distant objects clearly?
A)+80 cm, +1.3 diopters
B)-80 cm, +1.3 diopters
C)+80 cm, -1.3 diopters
D)-80 cm, -1.3 diopters
E)-1.3 cm, +1.3 diopters

Accepted Answer

The answer of A nearsighted person cannot see objects beyond...

Question 20

The focal length of a magnifying glass is 15 cm. If the near point of a person is 25 cm, what is the magnification of this glass for this person when his eyes are focused at infinity?
A)1.7
B)2.7
C)3.7
D)4.7
E)5.7

Accepted Answer

The answer of The focal length of a magnifying glass...

Quiz 33: Lenses and Optical Instruments

The objective lens of a refracting telescope has a focal length of 60 cm and the eyepiece a focal length of 8.0 cm. What is the angular magnification of the telescope?

What is the maximum possible magnification of the converging lens of focal length 5 cm?

A person can read the newspaper when it is held at 60 cm from his eyes. What should the focal length of his contact lenses be to allow him to read the newspaper comfortably at a distance of 30 cm?

What is the focal length of a pair of contact lenses that will allow a person with a near point of 125.0 cm to read a newspaper held 25.0 cm from his eyes?

Jill is farsighted and cannot see objects clearly that are closer to the eye than 80.0 cm. What is the focal length of the contact lenses that will enable her to see objects at a distance of 25.0 cm from her eyes?

What is the magnification of a magnifying glass of focal length 4.0 cm if the image is to be viewed by a relaxed eye with a near point of 25 cm?

Jill is farsighted and cannot see objects clearly that are closer to the eye than 80.0 cm. What is the refractive power of the contact lenses that will enable her to see objects at a distance of 25.0 cm from her eyes?

A nearsighted person has her distant vision corrected using a -2.0 D lens. Her uncorrected near point is 15 cm. What is her near point using this lens if the lens is 2.0 cm from the eye?

What power contact lens should be used to correct the vision of a farsighted person whose near point is 80 cm to see something clearly at a distance of 25 cm?

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

John is nearsighted and cannot see things beyond 90 cm from his eyes. What is the refractive power of the contact lenses that will enable him to see distant objects clearly?

A far sighted person can not see clearly objects that are closer to his eyes than 60.0 cm. Which one of the following combinations represents the correct focal length and the refractive power of the contact lenses that will enable him to see the objects at a distance of 25.0 cm from his eyes?

A magnifying glass produces an angular magnification of 7. What is the focal length of this lens if a person whose near point is 28 cm reads a book using this magnifying glass?

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

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 distant objects?

What is the near point of a farsighted person who can read a newspaper held 25 cm from his eyes when he wears 3.33 diopters glasses?

John is nearsighted and cannot see things beyond 110 cm from his eyes. What is the focal length of the contact lenses that will enable him to see distant objects clearly?

A magnifying glass uses a converging lens with a refractive power of 20 diopters. What is the magnification if the image is to be viewed by a relaxed eye with a near point of 25 cm?

A nearsighted person cannot see objects beyond 80 cm from his eyes. Which one of the following combinations represents the correct focal length and the refractive power of the contact lenses that will enable him to see the distant objects clearly?

The focal length of a magnifying glass is 15 cm. If the near point of a person is 25 cm, what is the magnification of this glass for this person when his eyes are focused at infinity?