Question 1

A camera lens has a focal length of 50.0 mm and an aperture setting of 4.00. What is the aperture diameter of this lens?

Accepted Answer

The aperture diameter can be calculated using the formula: Aperture Diameter = Focal Length / Aperture Setting. So, 50.0 mm / 4.00 = 12.5 mm.

Question 2

A person uses corrective glasses of power -8.5 D.
(a) Is this person nearsighted or farsighted?
(b) If the glasses are worn 2.0 cm from the eye, what is the person's far point without glasses?

Accepted Answer

The answer of A person uses corrective glasses of power...

Question 3

A magnifying glass of focal length 150. mm is used to examine an old manuscript.
(a) What is the maximum magnification given by the lens?
(b) What is the magnification for relaxed eye-viewing (image at infinity)?

Accepted Answer

The answer of A magnifying glass of focal length 150....

Question 4

A student wishes to build a telescope. She has available an eyepiece of focal length -5.0 cm. What focal length objective is needed to obtain a magnification of 10x?

Accepted Answer

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Question 5

What is the maximum angular magnification of a magnifying glass of focal length 10 cm?
 (Assume the near point is at 25 cm.)

Accepted Answer

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Question 6

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

Accepted Answer

The power of a lens (in diopters) is the inverse of the focal length (in meters). For a focal length of -40 cm, convert to meters (-0.4 m) and take the inverse: -1/0.4 = -2.5 diopters.

Question 7

A terrestrial telescope has focal lengths of 15. mm, 7.5 cm, and 120. cm for eyepiece, erecting lens, and objective respectively.
(a) What is the magnification of the telescope?
(b) Is this an angular magnification or a lateral size magnification?
(c) What is its length (objective to eyepiece distance)?

Accepted Answer

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Question 8

A person is nearsighted with a near point of 75. cm.
(a) What FOCAL LENGTH is this?
(b) What POWER lens is needed to correct their nearsightedness (assuming distance from lens to eye is negligible)?

Accepted Answer

The answer of A person is nearsighted with a near...

Question 9

A nearsighted person has a near point of 12. cm and a far point of 17. cm. If the lens is 2.0 cm from the eye:
(a) what lens power will enable this person to see distant objects clearly?
(b) what then will be the new near point?

Accepted Answer

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

Question 10

The focal length of a thin lens is 40 mm and its aperture diameter is 10 mm. What is the f-number of this lens?

Accepted Answer

The f-number (f/#) is calculated by dividing the focal length by the aperture diameter. Here, f/# = 40 mm / 10 mm = 4.0.

Question 11

The focal length of the lens of a simple camera is 40.0 mm. How far must the lens be moved to change the focus of the camera from a person 25 m away to one that is 4.0 m away?

Accepted Answer

The answer of The focal length of the lens of...

Question 12

Consider a magnifying glass with a power of 3.0 D.
(a) What is the maximum magnification for a person with a near point of 25. cm?
(b) What is the magnification when viewing with a relaxed eye?

Accepted Answer

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Question 13

What is the resolution limit at 400. nm, due to diffraction, of the Hubble Space Telescope which has an aperture of 2.4 meters?

Accepted Answer

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Question 14

A person's eye lens is 2.7 cm away from the retina. What must the focal length of this lens be in order for an object placed at the near point (N = 25.0 cm) of the eye to focus on the retina?

Accepted Answer

The lens formula is 1/f = 1/v - 1/u. Here, v = 2.7 cm (distance from lens to retina) and u = -25 cm (object distance, negative as per sign convention). Solving gives f = 2.4 cm.

Question 15

A person's eye lens is 2.8 cm away from the retina. What must the focal length of this lens be in order for an object placed at the far point of the eye to focus on the retina?

Accepted Answer

The focal length of the lens must be equal to the distance from the lens to the retina, which is 2.8 cm, for the image to be focused on the retina when the object is at the far point.

Question 16

A refracting telescope has an eyepiece of focal length -80. mm and an objective of focal length 36. cm. What is the magnification?

Accepted Answer

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Question 17

An objective lens of a telescope has a 1.90 m focal length. When viewed through this telescope, the moon appears 5.25 times larger than normal. How far apart are the objective lens and the eyepiece when this instrument is focused on the moon?

Accepted Answer

The answer of An objective lens of a telescope has...

Question 18

The world's largest refracting telescope is operated at the Yerkes Observatory in Wisconsin. It has an objective of diameter of 1.02 m. Suppose such an instrument could be mounted on a spy satellite at an elevation of 300. km above the surface of the Earth. What is the minimum separation of two objects on the ground if their images are to be clearly resolved by this lens?
 (Assume an average wavelength of 0.55 μm for white light.)

Accepted Answer

The answer of The world's largest refracting telescope is operated...

Question 19

What is the focal length of the corrective contact lens needed by a nearsighted person whose far point is 60 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) in diopters is P = 1/f (in meters), where f is the focal length. To make distant objects (at infinity) appear at the person's far point (60 cm or 0.6 meters), the lens must have a focal length of -0.6 meters or -60 cm. Negative because it's a diverging lens, suitable for nearsightedness correction.

Question 20

What is the power of the lens that has a focal length of 40 cm?

Accepted Answer

The power of a lens (in diopters) is the reciprocal of the focal length (in meters). For a focal length of 40 cm (0.4 meters), the power is 1/0.4 = +2.5 diopters.

Quiz 27: Optical Instruments

A camera lens has a focal length of 50.0 mm and an aperture setting of 4.00. What is the aperture diameter of this lens?

A person uses corrective glasses of power -8.5 D. (a) Is this person nearsighted or farsighted? (b) If the glasses are worn 2.0 cm from the eye, what is the person's far point without glasses?

A magnifying glass of focal length 150. mm is used to examine an old manuscript. (a) What is the maximum magnification given by the lens? (b) What is the magnification for relaxed eye-viewing (image at infinity)?