Question 1

The pupil of a cat's eye narrows to a slit of width 0.5 mm in daylight.Assuming a wavelength of 500 nm,what is the angular resolution? (1 nm = 10−⁹ m)

Accepted Answer

The angular resolution can be calculated using the formula θ = λ / D, where λ is the wavelength of light and D is the diameter of the aperture (in this case, the width of the pupil). Substituting λ = 500 nm (500 × 10^-9 m) and D = 0.5 mm (0.5 × 10^-3 m) into the formula gives θ = (500 × 10^-9 m) / (0.5 × 10^-3 m) = 1 × 10^-6 m/m = 1 × 10^-6 rad = 1 × 10^-6 rad, which simplifies to 1 × 10^-6 rad, matching choice A.

Question 2

A person can see well in the distance,but cannot do so at an arm's-length distance.To correct this,lenses that are ________ having a ________ power could be used.

Accepted Answer

The person can see well in the distance, which means they have a problem with nearsightedness. To correct nearsightedness, lenses that are thicker at their center than at the edges are used, which are known as convex or positive lenses. This type of lens helps divergent light rays that come from a near object to converge, so that they can be focused properly on the retina.

Question 3

The 2.4-m diameter Hubble space telescope has been placed into Earth orbit by the space shuttle.Assuming a wavelength of 684 nm,what angular resolution could this telescope achieve by Rayleigh's criterion? (1 nm = 10−⁹ m)

Accepted Answer

By Rayleigh's criterion, the angular resolution 𝜃 is given by 𝜃=1.22𝜆/D, where 𝜆 is the wavelength of light and D is the diameter of the telescope. Substituting the given values, we get 𝜃=1.22×684×10^-9/2.4=3.44×10^-7 rad. Rounding off to two significant figures, we get 𝜃=3.4×10^-7 rad, which corresponds to option D.

Question 4

A binary star system in the constellation Orion has an angular separation between the stars of 4*10−⁵ radians.Assuming a wavelength of 500 nm,what is the smallest aperture (diameter)telescope that will just resolve the two stars? (1 nm = 10−⁹ m)

Accepted Answer

We can use the Rayleigh criterion to determine the minimum angular separation required to resolve two point sources: 
θ ≈ 1.22 λ/D 
where θ is the angular separation, λ is the wavelength, and D is the diameter of the aperture (telescope). 
Rearranging this equation, we can solve for D: 
D = 1.22 λ/θ 
Plugging in θ = 4*10^-15 radians and λ = 500 nm (which is 5*10^-7 m), we get: 
D = 1.22 * 5*10^-7 m / (4*10^-15 radians) 
D ≈ 1.5 cm 
Therefore, the smallest aperture telescope that will just resolve the two stars is 1.5 cm in diameter. The answer is choice C.

Question 5

Using a camera with a fixed focal length lens,how will decreasing the f-number affect the depth of field and the intensity of the light reaching the ccd (or film)?

Accepted Answer

When the f-number is decreased, the aperture size increases which decreases the depth of field. However, the intensity of light reaching the CCD or film increases as the aperture size is larger, allowing more light to pass through.

Question 6

Which of the following primarily determines the resolution of a telescope?

Accepted Answer

The resolution of a telescope is primarily determined by the diameter of its objective lens or mirror, which affects the amount of light gathered and the angular resolution of the instrument. The other choices listed do not have as great of an impact on a telescope's resolution.

Question 7

The Michelson interferometer can make precise length measurements using which of the following phenomena?

Accepted Answer

The Michelson interferometer uses interference of light waves to make precise length measurements. By splitting a beam of light into two paths and recombining them, interference patterns are created that can reveal tiny differences in the lengths of the paths traveled by the light. Therefore, the correct choice is interference.

Question 8

How many lines in a grating must be illuminated to obtain a resolving power of 400 in a fourth-order spectrum?

Accepted Answer

The answer of How many lines in a grating must...

Question 9

If different filters are used with an astronomical telescope,which of the following would give the best resolution?

Accepted Answer

Green light has a shorter wavelength compared to red, yellow and purple light. Shorter wavelength light can provide better resolution as it diffracts less and produces sharp images. Therefore, using green filters with an astronomical telescope would give the best resolution.

Question 10

When using 545-nm light,how far is the adjustable mirror of a Michelson interferometer moved when 200 fringe shifts are counted?

Accepted Answer

The answer of When using 545-nm light,how far is the...

Question 11

Find the radius of a star image formed on the retina of the eye if the aperture diameter (the pupil)at night is 0.70 cm and the length of the eye is 3.2 cm.Assume the wavelength of starlight in the eye is 500 nm.(1 nm = 10−⁹ m)

Accepted Answer

The answer of Find the radius of a star image...

Question 12

What must be the resolving power of a grating allowing a spectral line at 683.80 nm to be distinguished from another line differing by 0.33 nm? (1 nm = 10−⁹ m)

Accepted Answer

The resolving power of a grating is given by the formula $R = \frac{\lambda}{\Delta \lambda}$, where $R$ is the resolving power, $\lambda$ is the wavelength of the light, and $\Delta \lambda$ is the difference in wavelength that needs to be resolved. Plugging in the given values, $R = \frac{683.80\,nm}{0.33\,nm} \approx 2072$, which rounds to the closest given option, 2,100.

Question 13

An individual's eye pupil changes from a diameter of 3.5 mm to 1.4 mm as the illumination is increased.By what factor does the minimum angle of resolution change?

Accepted Answer

The answer of An individual's eye pupil changes from a...

Question 14

The Michelson interferometer is a device that may be used to measure:

Accepted Answer

Michelson interferometer can be used to measure the wavelength of light by observing the interference pattern created by splitting a beam of light and recombining the two beams.

Question 15

The eye parts iris,retina,cornea,and ciliary muscle,play roles related to ________,________,________,and ________ in a camera.

Accepted Answer

The iris functions similarly to an aperture, controlling the amount of light that enters the eye, while the cornea and lens work together to focus the incoming light onto the retina (comparable to the CCD in a camera). The ciliary muscle adjusts the shape of the lens to change focus, which is also important in photography.

Question 16

What resolving power must a diffraction grating have in order to distinguish wavelengths of 686.30 nm and 687.50 nm? (1 nm = 10−⁹ m)

Accepted Answer

The resolving power of a diffraction grating is given by the equation R = Nm, where N is the number of lines per unit length and m is the order of diffraction. To distinguish between wavelengths of 686.30 nm and 687.50 nm, we need the difference in the angles of diffraction for these two wavelengths to be at least equal to the angle of minimum deviation. Using the equation nλ = d sinθ, where n is the order of diffraction, d is the spacing between the grating lines, and θ is the angle of diffraction, we can solve for the angle of diffraction for each wavelength. Taking the difference between these angles and setting it equal to the angle of minimum deviation, we get sinθ = 1/(2N). Rearranging the equation to solve for N, we get N = 1/(2 sinθ). Plugging in the values for the wavelengths and solving for N gives us N = 572 lines/mm. Therefore, the resolving power of the diffraction grating would be R = Nm = 572m. To distinguish between wavelengths of 686.30 nm and 687.50 nm, we need the difference in the angles of diffraction for these two wavelengths to be at least equal to the angle of minimum deviation. Using the equation nλ = d sinθ, where n is the order of diffraction, d is the spacing between the grating lines, and θ is the angle of diffraction, we can solve for the angle of diffraction for each wavelength. Taking the difference between these angles and setting it equal to the angle of minimum deviation, we get sinθ = 1/(2N). Rearranging the equation to solve for N, we get N = 1/(2 sinθ). Plugging in the values for the wavelengths and solving for N gives us N = 572 lines/mm. Therefore, the resolving power of the diffraction grating would be R = Nm = 572m.

Question 17

A fringe shift occurs for every ________ wavelength movement of the adjustable mirror in a Michelson interferometer.

Accepted Answer

The answer of A fringe shift occurs for every ________...

Question 18

Why is it easier to see fine print in brighter light than in dimmer light?

Accepted Answer

In brighter light, the pupil of the eye constricts, effectively increasing the f-number of the eye. This leads to a greater depth of field, allowing the eye to focus more easily on fine details such as small print.

Question 19

A magnifying lens of power d (in diopters)gives what magnification when the viewing eye is relaxed assuming a near point of 25 cm?

Accepted Answer

The magnifying power of a lens is given by M= 1+ (D/f), where D is the power of the lens in diopters and f is the focal length of the lens in meters. Here, since the near point is 25 cm or 0.25 meters, the focal length of the lens is f= 1/0.25 = 4 meters. Substituting this value in the magnification equation, we get M= 1+ (D/4) when the viewing eye is relaxed. Therefore, the magnification is directly proportional to the power of the lens, and the correct choice is C: d/4.

Quiz 25: Optical Instruments

The pupil of a cat's eye narrows to a slit of width 0.5 mm in daylight.Assuming a wavelength of 500 nm,what is the angular resolution? (1 nm = 10−⁹ m)

A person can see well in the distance,but cannot do so at an arm's-length distance.To correct this,lenses that are having a power could be used.

The 2.4-m diameter Hubble space telescope has been placed into Earth orbit by the space shuttle.Assuming a wavelength of 684 nm,what angular resolution could this telescope achieve by Rayleigh's criterion? (1 nm = 10−⁹ m)

A binary star system in the constellation Orion has an angular separation between the stars of 4*10−⁵ radians.Assuming a wavelength of 500 nm,what is the smallest aperture (diameter) telescope that will just resolve the two stars? (1 nm = 10−⁹ m)

Using a camera with a fixed focal length lens,how will decreasing the f-number affect the depth of field and the intensity of the light reaching the ccd (or film) ?

Which of the following primarily determines the resolution of a telescope?

The Michelson interferometer can make precise length measurements using which of the following phenomena?

How many lines in a grating must be illuminated to obtain a resolving power of 400 in a fourth-order spectrum?

If different filters are used with an astronomical telescope,which of the following would give the best resolution?

When using 545-nm light,how far is the adjustable mirror of a Michelson interferometer moved when 200 fringe shifts are counted?

Find the radius of a star image formed on the retina of the eye if the aperture diameter (the pupil) at night is 0.70 cm and the length of the eye is 3.2 cm.Assume the wavelength of starlight in the eye is 500 nm.(1 nm = 10−⁹ m)

What must be the resolving power of a grating allowing a spectral line at 683.80 nm to be distinguished from another line differing by 0.33 nm? (1 nm = 10−⁹ m)

An individual's eye pupil changes from a diameter of 3.5 mm to 1.4 mm as the illumination is increased.By what factor does the minimum angle of resolution change?

The Michelson interferometer is a device that may be used to measure:

The eye parts iris,retina,cornea,and ciliary muscle,play roles related to ,,,and in a camera.

What resolving power must a diffraction grating have in order to distinguish wavelengths of 686.30 nm and 687.50 nm? (1 nm = 10−⁹ m)

A fringe shift occurs for every ________ wavelength movement of the adjustable mirror in a Michelson interferometer.

Why is it easier to see fine print in brighter light than in dimmer light?

A magnifying lens of power d (in diopters) gives what magnification when the viewing eye is relaxed assuming a near point of 25 cm?

Quiz 25: Optical Instruments

The pupil of a cat's eye narrows to a slit of width 0.5 mm in daylight.Assuming a wavelength of 500 nm,what is the angular resolution? (1 nm = 10−9 m)

A person can see well in the distance,but cannot do so at an arm's-length distance.To correct this,lenses that are ________ having a ________ power could be used.

The 2.4-m diameter Hubble space telescope has been placed into Earth orbit by the space shuttle.Assuming a wavelength of 684 nm,what angular resolution could this telescope achieve by Rayleigh's criterion? (1 nm = 10−9 m)

A binary star system in the constellation Orion has an angular separation between the stars of 4*10−5 radians.Assuming a wavelength of 500 nm,what is the smallest aperture (diameter) telescope that will just resolve the two stars? (1 nm = 10−9 m)

Using a camera with a fixed focal length lens,how will decreasing the f-number affect the depth of field and the intensity of the light reaching the ccd (or film) ?

Which of the following primarily determines the resolution of a telescope?

The Michelson interferometer can make precise length measurements using which of the following phenomena?

How many lines in a grating must be illuminated to obtain a resolving power of 400 in a fourth-order spectrum?

If different filters are used with an astronomical telescope,which of the following would give the best resolution?

When using 545-nm light,how far is the adjustable mirror of a Michelson interferometer moved when 200 fringe shifts are counted?

Find the radius of a star image formed on the retina of the eye if the aperture diameter (the pupil) at night is 0.70 cm and the length of the eye is 3.2 cm.Assume the wavelength of starlight in the eye is 500 nm.(1 nm = 10−9 m)

What must be the resolving power of a grating allowing a spectral line at 683.80 nm to be distinguished from another line differing by 0.33 nm? (1 nm = 10−9 m)

An individual's eye pupil changes from a diameter of 3.5 mm to 1.4 mm as the illumination is increased.By what factor does the minimum angle of resolution change?

The Michelson interferometer is a device that may be used to measure:

The eye parts iris,retina,cornea,and ciliary muscle,play roles related to ________,________,________,and ________ in a camera.

What resolving power must a diffraction grating have in order to distinguish wavelengths of 686.30 nm and 687.50 nm? (1 nm = 10−9 m)

A fringe shift occurs for every ________ wavelength movement of the adjustable mirror in a Michelson interferometer.

Why is it easier to see fine print in brighter light than in dimmer light?

A magnifying lens of power d (in diopters) gives what magnification when the viewing eye is relaxed assuming a near point of 25 cm?

The pupil of a cat's eye narrows to a slit of width 0.5 mm in daylight.Assuming a wavelength of 500 nm,what is the angular resolution? (1 nm = 10−⁹ m)

A person can see well in the distance,but cannot do so at an arm's-length distance.To correct this,lenses that are having a power could be used.

The 2.4-m diameter Hubble space telescope has been placed into Earth orbit by the space shuttle.Assuming a wavelength of 684 nm,what angular resolution could this telescope achieve by Rayleigh's criterion? (1 nm = 10−⁹ m)

A binary star system in the constellation Orion has an angular separation between the stars of 4*10−⁵ radians.Assuming a wavelength of 500 nm,what is the smallest aperture (diameter) telescope that will just resolve the two stars? (1 nm = 10−⁹ m)

Find the radius of a star image formed on the retina of the eye if the aperture diameter (the pupil) at night is 0.70 cm and the length of the eye is 3.2 cm.Assume the wavelength of starlight in the eye is 500 nm.(1 nm = 10−⁹ m)

What must be the resolving power of a grating allowing a spectral line at 683.80 nm to be distinguished from another line differing by 0.33 nm? (1 nm = 10−⁹ m)

The eye parts iris,retina,cornea,and ciliary muscle,play roles related to ,,,and in a camera.

What resolving power must a diffraction grating have in order to distinguish wavelengths of 686.30 nm and 687.50 nm? (1 nm = 10−⁹ m)