Question 1

A zoom lens for a camera is adjusted to change its focal length from 38 mm to 304 mm. If
the same amount of light is to be admitted to the lens in both cases, what is the final
f-number if the original f-number was f/2.0?

Accepted Answer

The answer of A zoom lens for a camera is...

Question 2

A 35-mm camera equipped with a 45-mm focal length lens is used to photograph a tree 15 m tall. If the aperture of the lens is set at f/2, what is the aperture diameter?
A) 23 mm
B) 27 mm
C) 32 mm
D) 18 mm
E) 14 mm

Accepted Answer

The aperture diameter is given by the focal length divided by the f-number. In this case, the focal length is 45 mm and the f-number is f/2, so the aperture diameter is 45 mm / 2 = 22.5 mm.

Question 3

Light of wavelength 500 nm illuminates a round 0.50-mm-diameter hole. A screen is placed 6.0 m past the slit. What is the width of the central bright circle on the screen? 
A) $3700 \mu \mathrm { m }$
B) $7.3 \mathrm {~mm}$
C) $260 \mu \mathrm { m }$
D) $15 \mathrm {~mm}$

Accepted Answer

The width of the central bright circle (central maximum) in a diffraction pattern from a circular aperture is given by the formula $ \theta = 1.22 \frac{\lambda}{D} $, where $ \lambda $ is the wavelength and $ D $ is the diameter of the aperture. The linear width on the screen is $ 2L \tan(\theta) \approx 2L \theta $ for small angles, where $ L $ is the distance to the screen. Substituting the given values, the width is approximately 15 mm.

Question 4

A refracting telescope has a magnification M. If the focal length of the objective lens is doubled and the eyepiece focal length is halved, what is the new magnification? 
A) $M / 2$
B) $2 M$
C) $M / 4$
D) $M$
E) $4 M$

Accepted Answer

The magnification $M$ of a telescope is given by the ratio of the focal length of the objective lens ($f_o$) to the focal length of the eyepiece ($f_e$). If $f_o$ is doubled and $f_e$ is halved, the new magnification is $2f_o / (1/2f_e) = 4(f_o / f_e) = 4M$.

Question 5

A simple digital camera lens with focal length $f _ { O } = 3.00 \mathrm {~cm}$ perfectly focuses the image of an object on a CCD sensor located a distance $14.00 \mathrm {~cm}$ away from the lens. The object now moves away from the lens and the new distance between the lens and sensor is $13.00 \mathrm {~cm}$.
(a) By what amount did the object change its distance from the lens?
(b) What is the new magnification?
A) (a) $0.08 \mathrm {~cm}$
(b) $3.33$
B) (a) $0.03 \mathrm {~cm}$
(b) $0.30$
C) (a) $12.22 \mathrm {~cm}$
(b) $4.33$
D) (a) $990.00 \mathrm {~cm}$
(b) $0.23$

Accepted Answer

The object moved away from the lens by 1 cm. The new magnification is 3.33.

Question 6

If a metal sheet containing a tiny hole is heated (without damaging it) and therefore expands, what happens to the angular location of the first-order diffraction maximum?
A) It doesn't change.
B) It moves toward the centerline.
C) It moves away from the centerline.

Accepted Answer

When the metal sheet expands, the tiny hole also expands, increasing its diameter. According to the formula for diffraction maxima, $d \sin \theta = m\lambda$ (where $d$ is the diameter of the hole, $\theta$ is the angle to the maximum, $m$ is the order of the maximum, and $\lambda$ is the wavelength of the light), an increase in $d$ results in a decrease in $\sin \theta$ for the first-order maximum ($m = 1$), meaning $\theta$ decreases. Therefore, the first-order diffraction maximum moves toward the centerline.

Question 7

A simple refracting telescope provides large magnification by employing
A) a long focal length objective and a short focal length eyepiece.
B) a short focal length objective and a short focal length eyepiece.
C) a short focal length objective and a long focal length eyepiece.
D) a long focal length objective and a long focal length eyepiece.

Accepted Answer

The magnification of a simple refracting telescope is determined by the ratio of the focal length of the objective lens to that of the eyepiece. A long focal length objective and a short focal length eyepiece combination provides large magnification.

Question 8

A camera lens has a focal length of 50.0 mm and an aperture setting of f/4.00. What is the diameter of the aperture of this lens?
A) 200 mm
B) 12.5 mm
C) 25.0 mm
D) 35.4 mm
E) 10.1 mm

Accepted Answer

The diameter of the aperture can be calculated using the formula for the f-number: $f$-number = focal length / diameter of the aperture. Rearranging for the diameter gives: diameter = focal length / $f$-number = 50.0 mm / 4.00 = 12.5 mm.

Question 9

The focal length of the lens of a simple film camera is 40.0 mm. By what amount should the distance between the lens and the film be increased or decreased to change the focus from a
Person who is 25 m from the lens to one who is 4.0 m from the lens? 
A) $0.3 \mathrm {~mm}$
B) $0.5 \mathrm {~mm}$
C) $0.4 \mathrm {~mm}$
D) $0.2 \mathrm {~mm}$
E) $0.7 \mathrm {~mm}$

Accepted Answer

The lens equation is:$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$where f is the focal length, d_o is the object distance, and d_i is the image distance.When the person is 25 m from the lens, d_o = 25 m. When the person is 4.0 m from the lens, d_o = 4.0 m.We want to find the change in the image distance, d_i, when the object distance changes from 25 m to 4.0 m.$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$$$\frac{1}{40 \mathrm {~mm}} = \frac{1}{25 \mathrm {~m}} + \frac{1}{d_i}$$$$d_i = 40.4 \mathrm {~mm}$$$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$$$\frac{1}{40 \mathrm {~mm}} = \frac{1}{4 \mathrm {~m}} + \frac{1}{d_i}$$$$d_i = 40.7 \mathrm {~mm}$$The change in the image distance is:$$d_i - d_i = 40.7 \mathrm {~mm} - 40.4 \mathrm {~mm} = 0.3 \mathrm {~mm}$$Therefore, the distance between the lens and the film should be increased by 0.3 mm to change the focus from a person who is 25 m from the lens to one who is 4.0 m from the lens.

Question 10

The focal length of a camera lens is 40 mm and its aperture diameter is 10 mm. What is the f-number of this lens?
A) 0.25
B) 4.0
C) 0.40
D) 2.0
E) 5.6

Accepted Answer

The f-number of a lens is calculated by dividing the focal length by the aperture diameter. So, for a focal length of 40 mm and an aperture diameter of 10 mm, the f-number = 40 mm / 10 mm = 4.0.

Question 11

Light from a He-Ne laser of wavelength 633 nm passes through a circular aperture. The resulting pattern is observed on a screen 4.0 m behind the aperture, where the width of the central bright
Circle is 1.1 cm. What is the diameter of the hole? 
A) $4700 \mu \mathrm { m }$
B) $32,000 \mu \mathrm { m }$
C) $9.8 \mu \mathrm { m }$
D) $560 \mu \mathrm { m }$

Accepted Answer

The answer of Light from a He-Ne laser of wavelength...

Question 12

A 35-mm digital camera using a standard 50.0 mm lens is focused on a 1.80 m tall person
who is standing 3.25 m from the lens. You now refocus the camera on a 15.0 cm tall flower
that is 75.0 cm from the lens.
(a) In refocusing, by how much did you move the lens? Did you move it toward the film
or away from it?
(b) What is the height of the flower's image on the CCD sensor?

Accepted Answer

The answer of A 35-mm digital camera using a standard...

Question 13

Which one of the following is normally not a characteristic of a simple two-lens refracting astronomical telescope?
A) The objective forms a virtual image.
B) The final image is virtual.
C) The final image is inverted.
D) The angular size of the final image is larger than that of the object.

Accepted Answer

In a simple two-lens refracting astronomical telescope, the objective lens forms a real image, not a virtual image. This real image then acts as the object for the eyepiece lens, which magnifies it.

Question 14

Given perfect lenses, what is the main reason that a telescope with a large-diameter objective lens can produce a sharper image than one with a small-diameter lens?
A) A larger lens can focus more wavelengths of light than a smaller lens.
B) A larger lens has a longer focal length than a smaller lens.
C) A larger lens can focus more accurately than a smaller lens.
D) A larger lens can gather more light than a smaller lens.
E) There is less diffraction with a larger lens than with a smaller lens.

Accepted Answer

A larger lens reduces the effects of diffraction, leading to a sharper image.

Question 15

A $35 - \mathrm { mm }$ single lens reflex (SLR) digital camera is using a lens of focal length $35.0 \mathrm {~mm}$ to photograph a person who is $1.80 \mathrm {~m}$ tall and located $3.60 \mathrm {~m}$ from the lens.
(a) How far is the CCD sensor from the lens when the person is in focus?
(b) How tall is the person's image on the CCD sensor?

Accepted Answer

The answer of A $35 - \mathrm { mm }$...

Question 16

A slide projector needs to focus the image of a 24.0-mm × 36.0-mm slide onto a square
screen 1.50 m on each side. You want to fill the screen as completely as possible without
any of the image falling beyond the screen. Due to space constraints in the projector, the
slide must be placed 10.5 cm from the lens.
(a) What magnification does the projector produce?
(b) How far from the lens should the screen be placed?
(c) What focal length projector lens is needed?

Accepted Answer

The answer of A slide projector needs to focus the...

Question 17

A round 0.85-mm-diameter hole is illuminated by infrared light of wavelength 2.5 µm What is the angle of the first dark fringe in the resulting pattern? 
A) $4.8 \times 10 ^ { - 2 }$ degrees
B) $0.21$ degrees
C) $1.2 \times 10 ^ { - 2 }$ degrees
D) $3.6 \times 10 ^ { - 3 }$ degrees

Accepted Answer

The answer of A round 0.85-mm-diameter hole is illuminated by...

Question 18

You have a choice between two lenses of focal lengths fa and fb, where fb = 2fa, to use as the objective lens in building a refracting telescope. If the magnification you obtain using lens a is Ma,
What will be the magnification when using lens b? 
A) $M _ { b } = M _ { a } / 4$
B) $M _ { b } = 2 M _ { a }$
C) $M b = 8 M _ { a }$
D) $M _ { b } = 4 M _ { a }$
E) $M _ { b } = M _ { a } / 2$

Accepted Answer

The answer of You have a choice between two lenses...

Question 19

A $35 - \mathrm { mm }$ camera equipped with a $40 - \mathrm { mm }$ focal length lens is used to photograph a tree $17 \mathrm {~m}$ tall. If a 32-mm high image of the tree on the CCD sensor is required, how far should the camera lens be from the tree?
A) $22 \mathrm {~m}$
B) $26 \mathrm {~m}$
C) $21 \mathrm {~m}$
D) $23 \mathrm {~m}$
E) $24 \mathrm {~m}$

Accepted Answer

The answer of A $35 - \mathrm { mm }$...

Question 20

A lens of focal length $45 \mathrm {~mm}$ is mounted on a $35 - \mathrm { mm }$ camera. The lens aperture is set at $f / 2.0$ and the shutter speed set at $1 / 2000 \mathrm {~s}$. The photographer wants to keep the same exposure (amount of light), but wants to change the $f$-number to $f / 8.0$ for greater depth of field. What should be the new shutter speed to maintain the same exposure? 
A) $1 / 8000 \mathrm {~s}$
B) $1 / 1000 \mathrm {~s}$
C) $1 / 4000 \mathrm {~s}$
D) $1 / 125 \mathrm {~s}$
E) $1 / 500 \mathrm {~s}$

Accepted Answer

The answer of A lens of focal length \(45 \mathrm...

Quiz 25: Optical Instruments

A zoom lens for a camera is adjusted to change its focal length from 38 mm to 304 mm. If the same amount of light is to be admitted to the lens in both cases, what is the final f-number if the original f-number was f/2.0?

A 35-mm camera equipped with a 45-mm focal length lens is used to photograph a tree 15 m tall. If the aperture of the lens is set at f/2, what is the aperture diameter?

Light of wavelength 500 nm illuminates a round 0.50-mm-diameter hole. A screen is placed 6.0 m past the slit. What is the width of the central bright circle on the screen?

A refracting telescope has a magnification M. If the focal length of the objective lens is doubled and the eyepiece focal length is halved, what is the new magnification?

If a metal sheet containing a tiny hole is heated (without damaging it) and therefore expands, what happens to the angular location of the first-order diffraction maximum?

A simple refracting telescope provides large magnification by employing

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

The focal length of the lens of a simple film camera is 40.0 mm. By what amount should the distance between the lens and the film be increased or decreased to change the focus from a Person who is 25 m from the lens to one who is 4.0 m from the lens?

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

Light from a He-Ne laser of wavelength 633 nm passes through a circular aperture. The resulting pattern is observed on a screen 4.0 m behind the aperture, where the width of the central bright Circle is 1.1 cm. What is the diameter of the hole?

Which one of the following is normally not a characteristic of a simple two-lens refracting astronomical telescope?

Given perfect lenses, what is the main reason that a telescope with a large-diameter objective lens can produce a sharper image than one with a small-diameter lens?

A round 0.85-mm-diameter hole is illuminated by infrared light of wavelength 2.5 µm What is the angle of the first dark fringe in the resulting pattern?

You have a choice between two lenses of focal lengths fa and fb, where fb = 2fa, to use as the objective lens in building a refracting telescope. If the magnification you obtain using lens a is Ma, What will be the magnification when using lens b?

A 35−mm35 - \mathrm { mm }35−mm camera equipped with a 40−mm40 - \mathrm { mm }40−mm focal length lens is used to photograph a tree 17 m17 \mathrm {~m}17 m tall. If a 32-mm high image of the tree on the CCD sensor is required, how far should the camera lens be from the tree?

A $35 - \mathrm { mm }$ camera equipped with a $40 - \mathrm { mm }$ focal length lens is used to photograph a tree $17 \mathrm {~m}$ tall. If a 32-mm high image of the tree on the CCD sensor is required, how far should the camera lens be from the tree?