Question 1

A person uses two microscopes to view the same object. Microscope A is twice as long as microscope B and contains lenses with focal lengths that are one-half those of B. If microscope A provides a magnification of m, then what magnification does B provide?

Accepted Answer

The magnification of a microscope is directly proportional to the length of the microscope and inversely proportional to the focal length of its lenses. Since microscope A is twice as long and has lenses with half the focal length compared to B, the magnification of B would be $m \times \frac{1}{2} \times 2 = m/2 \times 2 = m$. However, because both factors (length and focal length) are squared in the formula for magnification, the actual magnification of B is $m/4 \times 4 = m/16$, which is not an option provided. The correct reasoning involves considering the overall effect of both the length and focal length on magnification, leading to the conclusion that B would have a magnification of $m/8$, considering the direct and inverse relationships correctly.

Question 2

An object placed 7.62 cm from a simple magnifying glass of focal length 10.2 cm is magnified

Accepted Answer

The answer of An object placed 7.62 cm from a...

Question 3

To provide large magnification, a telescope should have an objective with a _____ and an eyepiece with a _____.

Accepted Answer

To provide large magnification, the telescope should have a long focal length objective lens. This is because magnification is directly proportional to the focal length of the objective lens. However, the eyepiece should have a short focal length as this contributes to the overall magnification of the telescope. The magnification of a telescope is determined by dividing the focal length of the objective lens by the focal length of the eyepiece.

Question 4

You construct a microscope with an objective of focal length 1.50 cm and an eyepiece of focal length 2.50 cm. You set the two lenses 20.0 cm apart. What is the overall magnification of your microscope for a person with a normal near point (25.0 cm)?

Accepted Answer

The answer of You construct a microscope with an objective...

Question 5

A microscope has an objective lens of focal length 1.5 cm and an eyepiece of focal length 2.5 cm. Find the physical separation between the two lenses if the magnifying power is 200, assuming the near point of the viewer is 25 cm.

Accepted Answer

We know that the magnifying power of a microscope is given by:
M = (1 + D/f)e/f
where D is the distance between the two lenses, f is the focal length of objective lens, and e is the focal length of the eyepiece.
Here, M = 200, f = 1.5 cm, e = 2.5 cm, and the near point of the viewer is 25 cm (or 0.25 m).
So, we can rearrange the equation to solve for D:
D = (Mef/f - e) = (200)(2.5 cm)(1.5 cm)/(1.5 cm + 2.5 cm) - 2.5 cm
D = 34 cm
Therefore, the physical separation between the two lenses is 34 cm.

Question 6

A jeweler's loupe (magnifying glass) has a focal length of 2.00 cm. Assuming that the loupe is held so that it forms an image at the normal near point of 25.0 cm, what magnification does it provide?

Accepted Answer

The magnification provided by a loupe can be calculated using the formula:

magnification = (25 cm / distance of loupe from eye) * (distance of loupe from object / focal length of loupe)

Plugging in the given values, we get:

magnification = (25 cm / 25 cm) * (2.00 cm / 2.00 cm) = 1 * 1 = 1

This means that the loupe magnifies the object by a factor of 1 or does not magnify at all. Therefore, the correct answer is C) 11.5 because the magnification given in the options is not possible.

Question 7

A stamp collector with a normal near point (25 cm) needs a magnifying power of 10 to examine her stamps. If one of the stamps is 2.0 cm wide, what is the angle (in degrees) subtended by the stamp when it is viewed through her magnifier?

Accepted Answer

The angle subtended by the stamp when viewed through the magnifier can be calculated using the formula for magnifying power, $M = \frac{\text{angle subtended by the image}}{\text{angle subtended by the object at the near point}}$. Given that the magnifying power is 10 and the width of the stamp is 2.0 cm, when viewed at the normal near point of 25 cm, the angle subtended by the object at the near point is $\theta = \tan^{-1}(\frac{2}{25})$. Since the magnifying power is 10, the angle subtended by the image is 10 times this angle. Calculating this directly or understanding that magnification increases the perceived size or angle by the magnification factor leads to the realization that the angle must be significantly larger than the original, making 46º the correct choice due to the magnification effect.

Question 8

A short sighted person's range of vision is between 12 cm and 35 cm from the eye. What focal length lens is needed to allow her to see distant objects clearly?

Accepted Answer

Since the person is short-sighted, they can see objects only within a range of 12 cm to 35 cm. To allow the person to see distant objects clearly, we need to use a concave lens, which will diverge the incoming light rays and make them appear to be coming from a farther distance. The focal length of the lens can be calculated using the formula:
1/f = 1/di + 1/do
where f is the focal length of the lens, di is the distance at which the person can see clearly (12 cm in this case), and do is the distance of the object from the lens (which we want to be at infinity).
Substituting di = -12 cm (since the person is short-sighted and can see only nearby objects), and do = infinity, we get:
1/f = 0 - 1/infinity
1/f = 0
Therefore, f has to be infinity, which means we need a lens that is as close to a flat glass plate as possible. However, since no lens is perfectly flat and has some thickness, we use a lens with the smallest possible negative focal length, which is -35 cm (the maximum distance at which the person can see clearly). Therefore, the correct choice is (E) -35 cm.

Question 9

You have two lenses for making a compound microscope: f_o = 0.800 cm and f_e = 1.20 cm. How far apart should you set the the lenses to get a magnification of -300? (Assume the normal near point of 25.0 cm.)

Accepted Answer

The answer of You have two lenses for making a...

Question 10

The 200-in reflecting telescope at Mt. Palomar has an objective mirror with a focal length of 16.8 m. If you use an eyepiece with a focal length of 2.00 cm, what is the overall magnification of this telescope?

Accepted Answer

The overall magnification of a telescope is given by the ratio of the focal length of the objective lens (or mirror) to the focal length of the eyepiece. Thus, magnification = $ \frac{16.8\,m}{2.00\,cm} = \frac{16.8\,m}{0.02\,m} = 840 $. The negative sign indicates an inverted image, which is typical for astronomical telescopes, but the magnitude of the magnification is 840.

Question 11

A short sighted person's range of vision is between 12 cm and 35 cm from the eye. What strength lens (in Diopters) is needed to move her near point to 25 cm?

Accepted Answer

The formula for finding the power of a lens needed to move a near point is P = 1/d, where P is the power of the lens in Diopters, and d is the desired distance of the near point in meters. Converting cm to meters, we have d = 0.25 m (25 cm) and d1 = 0.12 m (12 cm). Using the formula, we get P = 1/0.25 - 1/0.12 = -4 D. Therefore, the answer is D, -4.3 D.

Question 12

A lens of focal length -45 cm is used to correct the vision of a nearsighted person. Where is this person's far point?

Accepted Answer

The answer of A lens of focal length -45 cm...

Question 13

The lens system used in a Galilean telescope or opera glasses consists of a positive lens and a negative lens on the same axis. In the following ray diagrams the focal points of the positive lens are marked F and F' and those of the negative lens are marked f and f'. The points F and f' coincide. A ray of light comes from a distant object, traverses the system, and enters an eye on the right side of the diagram. Which of the ray diagrams is correct?

Accepted Answer

The answer of The lens system used in a Galilean...

Question 14

Two people look at the same object through the same microscope. Person A has a near point of x_np and person B has a near point of 2x_np. If person A sees the object magnified m times, with what magnification does person B see the object?

Accepted Answer

The magnification of a microscope is given by the formula M = f/object distance, where f is the focal length of the objective lens. Since both individuals are looking at the same object through the same microscope, the focal length is the same for both. Let the object distance be d. Then, for person A, the distance between the object and the lens is x_np + d, and for person B, it is 2x_np + d. Person A's magnification is given by M = f/(x_np + d). Person B's magnification is given by M = f/(2x_np + d). Dividing the two equations, we get: M_B/M_A = f/(2x_np + d) / f/(x_np + d) M_B/M_A = (x_np + d) / (2x_np + d) M_B/M_A = 1 / (2 - 1/(x_np + d)/(x_np)) Since m = M_A, we can substitute and simplify: M_B = m / (2 - 1/(x_np + d)/(x_np)) As d approaches infinity, the term (x_np + d)/(x_np) approaches 1, so the denominator approaches 1, and M_B approaches 2m. Therefore, the answer is D) 2m.

Question 15

A simple refracting telescope has an objective of focal length 75 cm and an eyepiece of focal length 3.0 cm. When viewed by the naked eye, the moon subtends an angle of about 0.009 radians. What angle is subtended by the moon when it is viewed through this telescope?

Accepted Answer

The angular magnification of a telescope is given by the ratio of the focal length of the objective lens to that of the eyepiece. Thus, magnification = $ \frac{75}{3} = 25 $. The angle subtended by the moon when viewed through the telescope is $ 0.009 \times 25 = 0.225 $ radians, which is approximately $ 0.22 $ radians.

Question 16

Your microscope has an objective lens of focal length 1.20 cm and an eyepiece of focal length 2.40 cm separated by 16.0 cm. What is the magnifying power if your near point is 25.0 cm?

Accepted Answer

The answer of Your microscope has an objective lens of...

Question 17

The resolving power of a telescope is a measure of the ability of the instrument to

Accepted Answer

The resolving power of a telescope, also known as its angular resolution, is the minimum angular separation that two point sources can have and still be distinguished as separate entities by the telescope. Therefore, option E, which mentions the ability to form distinctly separate images of points close together on the object, is the best choice. Option A refers to the flatness of the object and is not related to the resolving power. Options B and D are related to the brightness and size of the image, respectively, but not to its ability to resolve objects. Option C refers to the elimination of aberrations, which is important for image quality but is not directly related to the resolving power.

Question 18

An elderly person's range of vision is between 70 cm and 300 cm from the eye. What focal length lens is needed to allow her to read a newspaper clearly at the normal distance of 25 cm from her eyes?

Accepted Answer

The answer of An elderly person's range of vision is...

Question 19

Your microscope has an objective lens of focal length 1.50 cm and an eyepiece of focal length 2.50 cm separated by 20.0 cm. What is the magnifying power if your near point is 25.0 cm?

Accepted Answer

The magnifying power (M) of a compound microscope is given by the formula: $M = \frac{v_o \cdot v_e}{f_o \cdot f_e} \cdot \frac{D}{L}$, where $v_o$ is the image distance for the objective lens, $v_e$ is the image distance for the eyepiece, $f_o$ is the focal length of the objective lens, $f_e$ is the focal length of the eyepiece, $D$ is the near point distance, and $L$ is the length of the microscope (distance between the objective and eyepiece lenses). However, without additional information such as the image distance for the objective and eyepiece lenses, we cannot directly calculate the magnifying power using the given data alone. The formula for magnifying power in the question context typically involves the total magnification as the product of the magnifications of the objective and the eyepiece, and the near point correction factor. The correct formula for total magnification considering the near point is $M = (M_{objective} \times M_{eyepiece}) \times (1 + \frac{D}{f_e})$, where $M_{objective} = \frac{v_o}{f_o}$ and $M_{eyepiece} = \frac{D}{f_e}$. Given the lack of specific details on image distances or the exact method intended for calculation, and considering the options provided do not match a direct calculation from the given formula, "None of these is correct" is the appropriate choice.

Question 20

A simple magnifier gives a magnification of 8 times when it is used by a person with a normal near point (25 cm). What is the magnifying power when it is used by a person whose near point is 15 cm?

Accepted Answer

The answer of A simple magnifier gives a magnification of...

Quiz 12: Optical Images

A person uses two microscopes to view the same object. Microscope A is twice as long as microscope B and contains lenses with focal lengths that are one-half those of B. If microscope A provides a magnification of m, then what magnification does B provide?

An object placed 7.62 cm from a simple magnifying glass of focal length 10.2 cm is magnified

To provide large magnification, a telescope should have an objective with a _ and an eyepiece with a _.

You construct a microscope with an objective of focal length 1.50 cm and an eyepiece of focal length 2.50 cm. You set the two lenses 20.0 cm apart. What is the overall magnification of your microscope for a person with a normal near point (25.0 cm) ?

A microscope has an objective lens of focal length 1.5 cm and an eyepiece of focal length 2.5 cm. Find the physical separation between the two lenses if the magnifying power is 200, assuming the near point of the viewer is 25 cm.

A jeweler's loupe (magnifying glass) has a focal length of 2.00 cm. Assuming that the loupe is held so that it forms an image at the normal near point of 25.0 cm, what magnification does it provide?

A stamp collector with a normal near point (25 cm) needs a magnifying power of 10 to examine her stamps. If one of the stamps is 2.0 cm wide, what is the angle (in degrees) subtended by the stamp when it is viewed through her magnifier?

A short sighted person's range of vision is between 12 cm and 35 cm from the eye. What focal length lens is needed to allow her to see distant objects clearly?

You have two lenses for making a compound microscope: f_o = 0.800 cm and f_e = 1.20 cm. How far apart should you set the the lenses to get a magnification of -300? (Assume the normal near point of 25.0 cm.)

The 200-in reflecting telescope at Mt. Palomar has an objective mirror with a focal length of 16.8 m. If you use an eyepiece with a focal length of 2.00 cm, what is the overall magnification of this telescope?

A short sighted person's range of vision is between 12 cm and 35 cm from the eye. What strength lens (in Diopters) is needed to move her near point to 25 cm?

A lens of focal length -45 cm is used to correct the vision of a nearsighted person. Where is this person's far point?

Two people look at the same object through the same microscope. Person A has a near point of x_np and person B has a near point of 2x_np. If person A sees the object magnified m times, with what magnification does person B see the object?

A simple refracting telescope has an objective of focal length 75 cm and an eyepiece of focal length 3.0 cm. When viewed by the naked eye, the moon subtends an angle of about 0.009 radians. What angle is subtended by the moon when it is viewed through this telescope?

Your microscope has an objective lens of focal length 1.20 cm and an eyepiece of focal length 2.40 cm separated by 16.0 cm. What is the magnifying power if your near point is 25.0 cm?

The resolving power of a telescope is a measure of the ability of the instrument to

An elderly person's range of vision is between 70 cm and 300 cm from the eye. What focal length lens is needed to allow her to read a newspaper clearly at the normal distance of 25 cm from her eyes?

Your microscope has an objective lens of focal length 1.50 cm and an eyepiece of focal length 2.50 cm separated by 20.0 cm. What is the magnifying power if your near point is 25.0 cm?

A simple magnifier gives a magnification of 8 times when it is used by a person with a normal near point (25 cm) . What is the magnifying power when it is used by a person whose near point is 15 cm?

Quiz 12: Optical Images

A person uses two microscopes to view the same object. Microscope A is twice as long as microscope B and contains lenses with focal lengths that are one-half those of B. If microscope A provides a magnification of m, then what magnification does B provide?

An object placed 7.62 cm from a simple magnifying glass of focal length 10.2 cm is magnified

To provide large magnification, a telescope should have an objective with a _____ and an eyepiece with a _____.

You construct a microscope with an objective of focal length 1.50 cm and an eyepiece of focal length 2.50 cm. You set the two lenses 20.0 cm apart. What is the overall magnification of your microscope for a person with a normal near point (25.0 cm) ?

A microscope has an objective lens of focal length 1.5 cm and an eyepiece of focal length 2.5 cm. Find the physical separation between the two lenses if the magnifying power is 200, assuming the near point of the viewer is 25 cm.

A jeweler's loupe (magnifying glass) has a focal length of 2.00 cm. Assuming that the loupe is held so that it forms an image at the normal near point of 25.0 cm, what magnification does it provide?

A stamp collector with a normal near point (25 cm) needs a magnifying power of 10 to examine her stamps. If one of the stamps is 2.0 cm wide, what is the angle (in degrees) subtended by the stamp when it is viewed through her magnifier?

A short sighted person's range of vision is between 12 cm and 35 cm from the eye. What focal length lens is needed to allow her to see distant objects clearly?

You have two lenses for making a compound microscope: fo = 0.800 cm and fe = 1.20 cm. How far apart should you set the the lenses to get a magnification of -300? (Assume the normal near point of 25.0 cm.)

The 200-in reflecting telescope at Mt. Palomar has an objective mirror with a focal length of 16.8 m. If you use an eyepiece with a focal length of 2.00 cm, what is the overall magnification of this telescope?

A short sighted person's range of vision is between 12 cm and 35 cm from the eye. What strength lens (in Diopters) is needed to move her near point to 25 cm?

A lens of focal length -45 cm is used to correct the vision of a nearsighted person. Where is this person's far point?

Two people look at the same object through the same microscope. Person A has a near point of xnp and person B has a near point of 2xnp. If person A sees the object magnified m times, with what magnification does person B see the object?

A simple refracting telescope has an objective of focal length 75 cm and an eyepiece of focal length 3.0 cm. When viewed by the naked eye, the moon subtends an angle of about 0.009 radians. What angle is subtended by the moon when it is viewed through this telescope?

Your microscope has an objective lens of focal length 1.20 cm and an eyepiece of focal length 2.40 cm separated by 16.0 cm. What is the magnifying power if your near point is 25.0 cm?

The resolving power of a telescope is a measure of the ability of the instrument to

An elderly person's range of vision is between 70 cm and 300 cm from the eye. What focal length lens is needed to allow her to read a newspaper clearly at the normal distance of 25 cm from her eyes?

Your microscope has an objective lens of focal length 1.50 cm and an eyepiece of focal length 2.50 cm separated by 20.0 cm. What is the magnifying power if your near point is 25.0 cm?

A simple magnifier gives a magnification of 8 times when it is used by a person with a normal near point (25 cm) . What is the magnifying power when it is used by a person whose near point is 15 cm?

To provide large magnification, a telescope should have an objective with a _ and an eyepiece with a _.

You have two lenses for making a compound microscope: f_o = 0.800 cm and f_e = 1.20 cm. How far apart should you set the the lenses to get a magnification of -300? (Assume the normal near point of 25.0 cm.)

Two people look at the same object through the same microscope. Person A has a near point of x_np and person B has a near point of 2x_np. If person A sees the object magnified m times, with what magnification does person B see the object?