Question 1

A 10-inch telescope is used to determine if what appears to be one star is actually two stars. Stars are so far away that they are essentially point sources. How close, in angle, can two stars be and still be resolved by this telescope? Use a wavelength of 550 nm.

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Question 2

What is the limiting angle of resolution for the eye if the pupil diameter of the eye is 4.0 mm, a wavelength of light of 600 nm and index of refraction for the eye equal to 1.34?

Accepted Answer

The limiting angle of resolution can be calculated using the formula θ = 1.22 * (λ / (n * D)), where λ is the wavelength of light, n is the index of refraction, and D is the diameter of the pupil. Substituting the given values, θ = 1.22 * (600 x 10^-9 m / (1.34 * 4.0 x 10^-3 m)) ≈ 1.4 × 10^-4 rad.

Question 3

A diffraction grating has 300 lines per mm. If light of wavelength 630 nm is sent through this grating, at what angle does the first order maximum occur?

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Question 4

A 200-m radio telescope is used to investigate sources emitting a 21-cm wavelength. The minimum angular separation resolvable for this system is

Accepted Answer

The minimum angular separation resolvable for a radio telescope is given by the Rayleigh criterion:$$	heta = 1.22 \frac{\lambda}{D}$$where $	heta$ is the angular separation, $\lambda$ is the wavelength, and $D$ is the diameter of the telescope.Plugging in the given values, we get:$$	heta = 1.22 \frac{0.21 	ext{ m}}{200 	ext{ m}} = 0.0013^\circ$$Therefore, the correct answer is C) 0.0013°.

Question 5

A diffraction grating has 5000 lines per cm. The angle between the central maximum and the fourth order maximum is 47.2°. What is the wavelength of the light?

Accepted Answer

The diffraction grating formula is d*sin(θ) = m*λ, where d is the distance between lines (1/5000 cm), θ is the angle (47.2°), m is the order (4), and λ is the wavelength. Solving for λ gives approximately 367 nm.

Question 6

The angular resolution of the eye is about 5 × 10^-4 rad. The Moon is about 400,000 km from the earth and has a diameter of about 3500 km. What is the smallest feature on the Moon that can be resolved with the unaided eye?

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Question 7

If the headlights on a car are separated by 1.3 m, how far down the road can they be resolved if the angular resolution of the eye is about 5 × 10^-4 rad?

Accepted Answer

The distance can be calculated using the formula for angular resolution: distance = separation / angular resolution. Substituting the given values, distance = 1.3 m / (5 × 10^-4 rad) = 2.6 km.

Question 8

In a diffraction experiment, light of 600 nm wavelength produces a first-order maximum 0.350 mm from the central maximum on a distant screen. A second monochromatic source produces a third-order maximum 0.870 mm from the central maximum when it passes through the same diffraction grating. What is the wavelength of the light from the second source?

Accepted Answer

The position of maxima in a diffraction pattern is given by $ y = \frac{m \lambda L}{d} $, where $ m $ is the order, $ \lambda $ is the wavelength, $ L $ is the distance to the screen, and $ d $ is the grating spacing. For the first source, $ y_1 = 0.350 $ mm, $ m_1 = 1 $, and $ \lambda_1 = 600 $ nm. For the second source, $ y_2 = 0.870 $ mm and $ m_2 = 3 $. Using the ratio $ \frac{y_2}{y_1} = \frac{m_2 \lambda_2}{m_1 \lambda_1} $, we find $ \lambda_2 = \frac{y_2 \cdot m_1 \cdot \lambda_1}{y_1 \cdot m_2} = \frac{0.870 \cdot 1 \cdot 600}{0.350 \cdot 3} = 497 $ nm.

Question 9

The limiting angle of resolution for the eye is 1.4 × 10^-4 rad. What is the minimum separation between two point sources of light that the eye can distinguish if they are at a distance of 40 m from the observer?

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Question 10

Monochromatic light is incident on a grating that is 75 mm wide and ruled with 50,000 lines. The second-order maximum is seen at 32.5°. What is the wavelength of the incident light?

Accepted Answer

We can use the grating equation:
$n\lambda=d\sin(	heta)$, where $n$ is the order of the maximum, $d$ is the spacing between the grating lines, $	heta$ is the angle of diffraction, and $\lambda$ is the wavelength of the incident light.

Since the second-order maximum is seen, $n = 2$. We are given that $d=1/50000$ lines/mm $= 2 	imes 10^{-5}$ mm, and $	heta = 32.5^\circ$. We need to convert the angle to radians, so $	heta = \frac{32.5}{180}\pi \approx 0.567$ rad.

Solving for $\lambda$, we get $\lambda = \frac{d\sin(	heta)}{n} = \frac{(2 	imes 10^{-5} 	ext{ mm})(\sin(0.567))}{2} \approx 4.03 	imes 10^{-7}$ mm $= 403$ nm.

Therefore, the best choice is B, as it matches the calculation above.

Question 11

A He-Ne laser (632.8 nm) is used to calibrate a grating. If the first-order maximum occurs at 20.5°, what is the grating constant (the distance between the slits)?

Accepted Answer

The grating equation is d*sin(θ) = m*λ, where d is the grating constant, θ is the angle, m is the order, and λ is the wavelength. For the first-order maximum (m=1), d = λ/sin(θ) = 632.8 nm / sin(20.5°) = 1.81 μm.

Question 12

White light is spread out into spectral hues by a grating. If the grating has 2000 lines per centimeter, at what angle will red light (640 nm) appear in the first order?

Accepted Answer

The angle for the first order can be calculated using the grating equation: d*sin(θ) = m*λ, where d is the distance between grating lines (1/2000 cm), m is the order (1), and λ is the wavelength (640 nm or 640 x 10^-7 cm). Solving for θ gives approximately 7.35°.

Question 13

A certain astronomical telescope has a diameter of 5.60 m. What is the minimum angle of resolution for this telescope at a wavelength of 620 nm?

Accepted Answer

The minimum angle of resolution can be calculated using the formula θ = 1.22 * (λ/D), where λ is the wavelength and D is the diameter. Substituting the given values, θ = 1.22 * (620 x 10^-9 m / 5.60 m) = 1.35 × 10^-7 rad.

Question 14

A diffraction grating has 300 lines per mm. If light of wavelength 630 nm is sent through this grating, what is the highest order maximum that will appear?

Accepted Answer

The formula for finding the highest order maximum is given as:

n(max) = d / λ
where:
d = distance between adjacent slits (which is equal to 1/300 mm for this grating)
λ = wavelength of light (which is given as 630 nm)

Thus, n(max) = (1/300 mm) / (630 nm) = 5.03

Since n(max) must be a whole number, the highest order maximum that will appear is 5.

Question 15

Monochromatic light of wavelength 500 nm is incident normally on a grating. If the third-order maximum of the diffraction pattern is observed at 32.0°, what is the grating constant (distance between the slits)?

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Question 16

What resolving power is needed to resolve spectral lines at 651.22 nm and 651.81 nm?

Accepted Answer

The resolving power R is given by R = λ/Δλ, where λ is the average wavelength and Δλ is the difference between the wavelengths. Here, λ = (651.22 + 651.81)/2 = 651.515 nm and Δλ = 651.81 - 651.22 = 0.59 nm. Thus, R = 651.515 / 0.59 ≈ 1104, which is closest to 1100.

Question 17

A telescope that uses a mirror 249 cm in diameter is just able to resolve a double-star system that is 1.5 light-years away. Assume the light from the stars has a wavelength of 691 nm. How far apart are the two stars? One light year = 9.46 × 10¹⁵ m. (Use the approximation for θ_min: θ_min ≈ .)

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Question 18

Monochromatic light of wavelength 500 nm is incident normally on a grating. If the third-order maximum of the diffraction pattern is observed at 32.0°, how many total number of maxima can be seen?

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Question 19

A diffraction grating has 6000 lines per centimeter ruled on it. What is the angular separation between the second and the third orders on the same side of the central order when the grating is illuminated with a beam of light of wavelength 550 nm?

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Question 20

When light illuminates a grating with 7000 lines per centimeter, its second order maximum is at 62.4°. What is the wavelength of the light?

Accepted Answer

The grating equation is d*sin(θ) = m*λ, where d is the distance between lines (1/7000 cm), θ is the angle (62.4°), m is the order (2), and λ is the wavelength. Solving for λ gives approximately 633 nm.

Quiz 35: Diffraction and Polarization

A 10-inch telescope is used to determine if what appears to be one star is actually two stars. Stars are so far away that they are essentially point sources. How close, in angle, can two stars be and still be resolved by this telescope? Use a wavelength of 550 nm.

What is the limiting angle of resolution for the eye if the pupil diameter of the eye is 4.0 mm, a wavelength of light of 600 nm and index of refraction for the eye equal to 1.34?

A diffraction grating has 300 lines per mm. If light of wavelength 630 nm is sent through this grating, at what angle does the first order maximum occur?

A 200-m radio telescope is used to investigate sources emitting a 21-cm wavelength. The minimum angular separation resolvable for this system is

A diffraction grating has 5000 lines per cm. The angle between the central maximum and the fourth order maximum is 47.2°. What is the wavelength of the light?

The angular resolution of the eye is about 5 × 10^-4 rad. The Moon is about 400,000 km from the earth and has a diameter of about 3500 km. What is the smallest feature on the Moon that can be resolved with the unaided eye?

If the headlights on a car are separated by 1.3 m, how far down the road can they be resolved if the angular resolution of the eye is about 5 × 10^-4 rad?

The limiting angle of resolution for the eye is 1.4 × 10^-4 rad. What is the minimum separation between two point sources of light that the eye can distinguish if they are at a distance of 40 m from the observer?

Monochromatic light is incident on a grating that is 75 mm wide and ruled with 50,000 lines. The second-order maximum is seen at 32.5°. What is the wavelength of the incident light?

A He-Ne laser (632.8 nm) is used to calibrate a grating. If the first-order maximum occurs at 20.5°, what is the grating constant (the distance between the slits) ?

White light is spread out into spectral hues by a grating. If the grating has 2000 lines per centimeter, at what angle will red light (640 nm) appear in the first order?

A certain astronomical telescope has a diameter of 5.60 m. What is the minimum angle of resolution for this telescope at a wavelength of 620 nm?

A diffraction grating has 300 lines per mm. If light of wavelength 630 nm is sent through this grating, what is the highest order maximum that will appear?

Monochromatic light of wavelength 500 nm is incident normally on a grating. If the third-order maximum of the diffraction pattern is observed at 32.0°, what is the grating constant (distance between the slits) ?

What resolving power is needed to resolve spectral lines at 651.22 nm and 651.81 nm?

Monochromatic light of wavelength 500 nm is incident normally on a grating. If the third-order maximum of the diffraction pattern is observed at 32.0°, how many total number of maxima can be seen?

A diffraction grating has 6000 lines per centimeter ruled on it. What is the angular separation between the second and the third orders on the same side of the central order when the grating is illuminated with a beam of light of wavelength 550 nm?

When light illuminates a grating with 7000 lines per centimeter, its second order maximum is at 62.4°. What is the wavelength of the light?

Quiz 35: Diffraction and Polarization

A 10-inch telescope is used to determine if what appears to be one star is actually two stars. Stars are so far away that they are essentially point sources. How close, in angle, can two stars be and still be resolved by this telescope? Use a wavelength of 550 nm.

What is the limiting angle of resolution for the eye if the pupil diameter of the eye is 4.0 mm, a wavelength of light of 600 nm and index of refraction for the eye equal to 1.34?

A diffraction grating has 300 lines per mm. If light of wavelength 630 nm is sent through this grating, at what angle does the first order maximum occur?

A 200-m radio telescope is used to investigate sources emitting a 21-cm wavelength. The minimum angular separation resolvable for this system is

A diffraction grating has 5000 lines per cm. The angle between the central maximum and the fourth order maximum is 47.2°. What is the wavelength of the light?

The angular resolution of the eye is about 5 × 10-4 rad. The Moon is about 400,000 km from the earth and has a diameter of about 3500 km. What is the smallest feature on the Moon that can be resolved with the unaided eye?

If the headlights on a car are separated by 1.3 m, how far down the road can they be resolved if the angular resolution of the eye is about 5 × 10-4 rad?

The limiting angle of resolution for the eye is 1.4 × 10-4 rad. What is the minimum separation between two point sources of light that the eye can distinguish if they are at a distance of 40 m from the observer?

Monochromatic light is incident on a grating that is 75 mm wide and ruled with 50,000 lines. The second-order maximum is seen at 32.5°. What is the wavelength of the incident light?

A He-Ne laser (632.8 nm) is used to calibrate a grating. If the first-order maximum occurs at 20.5°, what is the grating constant (the distance between the slits) ?

White light is spread out into spectral hues by a grating. If the grating has 2000 lines per centimeter, at what angle will red light (640 nm) appear in the first order?

A certain astronomical telescope has a diameter of 5.60 m. What is the minimum angle of resolution for this telescope at a wavelength of 620 nm?

A diffraction grating has 300 lines per mm. If light of wavelength 630 nm is sent through this grating, what is the highest order maximum that will appear?

Monochromatic light of wavelength 500 nm is incident normally on a grating. If the third-order maximum of the diffraction pattern is observed at 32.0°, what is the grating constant (distance between the slits) ?

What resolving power is needed to resolve spectral lines at 651.22 nm and 651.81 nm?

A telescope that uses a mirror 249 cm in diameter is just able to resolve a double-star system that is 1.5 light-years away. Assume the light from the stars has a wavelength of 691 nm. How far apart are the two stars? One light year = 9.46 × 1015 m. (Use the approximation for θmin: θmin ≈ .)

Monochromatic light of wavelength 500 nm is incident normally on a grating. If the third-order maximum of the diffraction pattern is observed at 32.0°, how many total number of maxima can be seen?

A diffraction grating has 6000 lines per centimeter ruled on it. What is the angular separation between the second and the third orders on the same side of the central order when the grating is illuminated with a beam of light of wavelength 550 nm?

When light illuminates a grating with 7000 lines per centimeter, its second order maximum is at 62.4°. What is the wavelength of the light?

The angular resolution of the eye is about 5 × 10^-4 rad. The Moon is about 400,000 km from the earth and has a diameter of about 3500 km. What is the smallest feature on the Moon that can be resolved with the unaided eye?

If the headlights on a car are separated by 1.3 m, how far down the road can they be resolved if the angular resolution of the eye is about 5 × 10^-4 rad?

The limiting angle of resolution for the eye is 1.4 × 10^-4 rad. What is the minimum separation between two point sources of light that the eye can distinguish if they are at a distance of 40 m from the observer?