Question 1

The Hubble Space Telescope in orbit above the Earth has a 2.4 m circular aperture. The telescope has equipment for detecting ultraviolet light. What is the minimum angular separation between two objects that the Hubble Space Telescope can resolve in ultraviolet light of wavelength 95 nm?

Accepted Answer

The Rayleigh criterion for the minimum angular separation between two objects that can be resolved by a circular aperture is:$$	heta = 1.22 \frac{\lambda}{D}$$where:$$	heta$$ is the minimum angular separation$$\lambda$$ is the wavelength of light$$D$$ is the diameter of the aperturePlugging in the given values, we get:$$	heta = 1.22 \frac{95 	ext{ nm}}{2.4 	ext{ m}} = 4.8 	imes 10^{-8} 	ext{ rad}$$Therefore, the correct answer is A.

Question 2

Red light of wavelength 600.0 nm is incident on a grating. If the separation between the slits is 5.0 × 10^-⁵ m, at what angle does the first principal maximum occur?

Accepted Answer

The formula for the angle of diffraction of a grating is given by:
$sin θ = \frac{mλ}{d}$
where m is the order of diffraction, λ is the wavelength of light, and d is the separation between the slits.
For the first principal maximum, m = 1. Substituting the given values, we get:
$sin θ = \frac{1 × 600.0 × 10^{-9} m}{5.0 × 10^{-6} m} = 0.12$
Taking the inverse sine of both sides, we get:
$θ = sin^{-1} (0.12) = 1.2 × 10^{-1} rad = 1.2 × 10^{-1} × \frac{180}{\pi}° = 6.9°$
Therefore, the answer is C) 1.2 × 10^-1 rad, or approximately 0.69°.

Question 3

Light from two sources, $\lambda$₁ = 623 nm and $\lambda$₂ = 488 nm, is incident on a diffraction grating that has 5550 lines/cm. What is the angular separation, $\theta$₁ - $\theta$₂, of the second order maxima of the two waves?

Accepted Answer

The answer of Light from two sources, $\lambda$₁ = 623...

Question 4

When light with a wavelength of 425 nm uniformly illuminates a single slit, the central bright fringe, observed on a screen located 0.630 m from the slit, has a width of 0.0166 m. What is the width of the slit?

Accepted Answer

The width of the central bright fringe is given by the formula: width = 2 * (wavelength * distance to screen) / slit width. Solving for the slit width gives: slit width = 2 * (425 nm * 0.630 m) / 0.0166 m = 3.23 × 10^-5 m.

Question 5

Two stars are just barely resolved by a telescope with a lens diameter of 0.500 m. Determine the angular separation of the two stars. Assume incident light of wavelength 500.0 nm.

Accepted Answer

The angular separation of the two stars is given by the Rayleigh criterion:$$	heta = 1.22 \frac{\lambda}{D}$$where $\lambda$ is the wavelength of light and $D$ is the diameter of the lens. Substituting the given values, we get:$$	heta = 1.22 \frac{500.0 	imes 10^{-9} 	ext{ m}}{0.500 	ext{ m}} = 1.22 	imes 10^{-6} 	ext{ rad}$$

Question 6

A spy satellite is in orbit at a distance of 1.0 × 10⁶ m above the ground. It carries a telescope that can resolve the two rails of a railroad track that are 1.4 m apart using light of wavelength 600 nm. Which one of the following statements best describes the diameter of the lens in the telescope?

Accepted Answer

The resolving power of a telescope is determined by the Rayleigh criterion, which states that the minimum resolvable angle θ is approximately 1.22(λ/D), where λ is the wavelength and D is the diameter of the lens. Given the distance and separation, the diameter must be large enough to resolve the 1.4 m separation at 1.0 × 10^6 m distance, which requires a diameter greater than 0.52 m.

Question 7

Light from a laser ($\lambda$= 640 nm) passes through a diffraction grating and spreads out into three beams as shown in the figure. Determine the spacing between the slits of the grating.

Accepted Answer

The answer of Light from a laser ($\lambda$= 640 nm)...

Question 8

Light of wavelength 530 nm is incident on two slits that are spaced 1.0 mm apart. If each of the slits has a width of 0.10 mm, how many interference maxima lie within the central diffraction peak?

Accepted Answer

The answer of Light of wavelength 530 nm is incident...

Question 9

Two candles are lit and separated by 0.10 m. If the diameter of the pupil of an observer's eye is 3.5 mm, what is the maximum distance that the candles can be away from the observer and be seen as two light sources? Use 545 nm for the wavelength of light in the eye.

Accepted Answer

According to Rayleigh's criterion, two light sources can be distinguished if the central maximum of one source falls on the first minimum of the other. This occurs when the angle between the two sources is:
sin θ = 1.22 λ/D
where λ is the wavelength of the light, D is the diameter of the pupil, and θ is the angular separation between the two sources.

Rearranging this formula, we get:
D = 1.22 λ/sin θ

For the given problem, θ = tan-1(0.05/0.10) = 26.57° (the distance between the candles is equal to the tangent of the angular separation angle)
Plugging in the values, we get:
D = 1.22 x 545 x 10^-9 / sin 26.57°
D ≈ 3.4 x 10^-6 m

Therefore, for the observer to distinguish the two light sources, the maximum distance between the candles can be:
distance = D / tan θ
distance = (3.4 x 10^-6) / tan 26.57°
distance ≈ 528 m

Thus, the best choice is (C) 530 m.

Question 10

Visible light of wavelength 589 nm is incident on a diffraction grating that has 3500 lines/cm. At what angle with respect to the central maximum is the fifth order maximum observed?

Accepted Answer

The angle for the fifth order maximum can be calculated using the diffraction grating formula: d*sin(θ) = m*λ, where d is the distance between grating lines (1/3500 cm), m is the order number (5), and λ is the wavelength (589 nm). Solving for sin(θ) gives a value greater than 1, which is not possible, indicating that a fifth order maximum cannot be observed.

Question 11

A diffraction grating that has 4500 lines/cm is illuminated by light that has a single wavelength. If a second order maximum is observed at an angle of 42° with respect to the central maximum, what is the wavelength of this light?

Accepted Answer

The diffraction grating equation is d*sin(θ) = m*λ, where d is the distance between grating lines (1/4500 cm), θ is the angle (42°), m is the order (2), and λ is the wavelength. Solving for λ gives approximately 740 nm.

Question 12

White light is passed through a diffraction grating that has 2.50 × 10⁵ lines/m. On each side of the white central maximum, a spectrum of colors is observed. What is the wavelength of the light observed at an angle of 7.00° in the first-order bright fringes?

Accepted Answer

The correct answer is A because the wavelength of the light observed at an angle of 7.00° in the first-order bright fringes is 487 nm.

Question 13

A 30.0-mm wide diffraction grating produces a deviation of 30.0° in the second order principal maxima. The wavelength of light is 600.0 nm. What is the total number of slits on the grating?

Accepted Answer

The formula for diffraction grating is: 
d(sinθ + sinθ') = mλ 
where 
d = distance between the slits (grating space), 
θ = angle of incidence, 
θ' = angle of diffraction, 
m = order of maxima 
λ = wavelength.

In this question, 
d = 30.0 mm = 0.03 m (given), 
θ' = 30.0° (given), 
m = 2 (second order maxima), 
λ = 600.0 nm = 6.00 x 10^-7 m

Hence, we can rearrange the formula to find the number of slits: 
n = d/λ = (sinθ + sinθ')/mλ

n = 12.5 x 10^3 = 12,500

Therefore, the total number of slits on the grating is 12,500. 
The correct answer is (C).

Question 14

The headlights of a car are 1.6 m apart and produce light of wavelength 575 nm in vacuum. The pupil of the eye of the observer has a diameter of 4.0 mm and a refractive index of 1.4. What is the maximum distance from the observer that the two headlights can be distinguished?

Accepted Answer

The answer of The headlights of a car are 1.6...

Question 15

Which one of the following statements provides the most convincing evidence that electromagnetic waves have a transverse character?

Accepted Answer

The fact that electromagnetic waves can be polarized provides the most convincing evidence that they have a transverse character. Polarization refers to the orientation of the electric and magnetic fields of a wave, and transverse waves are the only type of wave that can be polarized. The other options (refraction, reflection, diffraction, and interference) are all properties that can be exhibited by both transverse and longitudinal waves.

Question 16

The wavelength of light emitted from two distant objects is 715 nm. What is the minimum angle at which these objects can just be resolved when using binoculars with a 50-mm objective lens?

Accepted Answer

To resolve two objects, the minimum angle of separation between them should be:
$	heta = 1.22\frac{\lambda}{D}$
where $\lambda$ is the wavelength of light and $D$ is the diameter of the objective lens.
Substituting $\lambda = 715	ext{ nm} = 7.15	imes 10^{-7}	ext{ m}$ and $D = 50	ext{ mm} = 5	imes 10^{-2}	ext{ m}$, we get:
$	heta = 1.22\frac{7.15	imes 10^{-7}}{5	imes 10^{-2}} \approx 1.73	imes 10^{-5}	ext{ radians}$
Converting to degrees:
$	heta \approx 0.99'' \approx \boxed{	extbf{(B) }10.1	ext{ degrees}}$ (rounded to one decimal place)

Question 17

A beam of light that consists of a mixture of red light ($\lambda$ = 660 nm in vacuum) and violet light ($\lambda$ = 410 nm in vacuum) falls on a grating that contains 1.0 × 10⁴ lines/cm. Find the angular separation between the first-order maxima of the two wavelengths if the experiment takes place in a vacuum.

Accepted Answer

The angular separation between the first-order maxima can be found using the grating equation $d \sin \theta = m \lambda$, where $d$ is the distance between the lines on the grating, $\theta$ is the angle, $m$ is the order of the maximum, and $\lambda$ is the wavelength. For the first-order maxima ($m=1$), calculate $\theta$ for both wavelengths and find the difference. The grating spacing $d = 1/(1.0 \times 10^4 \text{ lines/cm}) = 1 \times 10^{-6} \text{ m}$. For red light, $\theta_r = \arcsin((660 \times 10^{-9})/(1 \times 10^{-6}))$, and for violet light, $\theta_v = \arcsin((410 \times 10^{-9})/(1 \times 10^{-6}))$. The angular separation is $\theta_r - \theta_v \approx 17^\circ$.

Quiz 27: Interference and the Wave Nature of Light

The Hubble Space Telescope in orbit above the Earth has a 2.4 m circular aperture. The telescope has equipment for detecting ultraviolet light. What is the minimum angular separation between two objects that the Hubble Space Telescope can resolve in ultraviolet light of wavelength 95 nm?

Red light of wavelength 600.0 nm is incident on a grating. If the separation between the slits is 5.0 × 10^-⁵ m, at what angle does the first principal maximum occur?

Light from two sources, $\lambda$ ₁ = 623 nm and $\lambda$ ₂ = 488 nm, is incident on a diffraction grating that has 5550 lines/cm. What is the angular separation, $\theta$ ₁ - $\theta$ ₂, of the second order maxima of the two waves?

When light with a wavelength of 425 nm uniformly illuminates a single slit, the central bright fringe, observed on a screen located 0.630 m from the slit, has a width of 0.0166 m. What is the width of the slit?

Two stars are just barely resolved by a telescope with a lens diameter of 0.500 m. Determine the angular separation of the two stars. Assume incident light of wavelength 500.0 nm.

Light of wavelength 530 nm is incident on two slits that are spaced 1.0 mm apart. If each of the slits has a width of 0.10 mm, how many interference maxima lie within the central diffraction peak?

Two candles are lit and separated by 0.10 m. If the diameter of the pupil of an observer's eye is 3.5 mm, what is the maximum distance that the candles can be away from the observer and be seen as two light sources? Use 545 nm for the wavelength of light in the eye.

Visible light of wavelength 589 nm is incident on a diffraction grating that has 3500 lines/cm. At what angle with respect to the central maximum is the fifth order maximum observed?

A diffraction grating that has 4500 lines/cm is illuminated by light that has a single wavelength. If a second order maximum is observed at an angle of 42° with respect to the central maximum, what is the wavelength of this light?

White light is passed through a diffraction grating that has 2.50 × 10⁵ lines/m. On each side of the white central maximum, a spectrum of colors is observed. What is the wavelength of the light observed at an angle of 7.00° in the first-order bright fringes?

A 30.0-mm wide diffraction grating produces a deviation of 30.0° in the second order principal maxima. The wavelength of light is 600.0 nm. What is the total number of slits on the grating?

The headlights of a car are 1.6 m apart and produce light of wavelength 575 nm in vacuum. The pupil of the eye of the observer has a diameter of 4.0 mm and a refractive index of 1.4. What is the maximum distance from the observer that the two headlights can be distinguished?

Which one of the following statements provides the most convincing evidence that electromagnetic waves have a transverse character?

The wavelength of light emitted from two distant objects is 715 nm. What is the minimum angle at which these objects can just be resolved when using binoculars with a 50-mm objective lens?

Quiz 27: Interference and the Wave Nature of Light

The Hubble Space Telescope in orbit above the Earth has a 2.4 m circular aperture. The telescope has equipment for detecting ultraviolet light. What is the minimum angular separation between two objects that the Hubble Space Telescope can resolve in ultraviolet light of wavelength 95 nm?

Red light of wavelength 600.0 nm is incident on a grating. If the separation between the slits is 5.0 × 10-5 m, at what angle does the first principal maximum occur?

Light from two sources, λ\lambdaλ 1 = 623 nm and λ\lambdaλ 2 = 488 nm, is incident on a diffraction grating that has 5550 lines/cm. What is the angular separation, θ\thetaθ 1 - θ\thetaθ 2, of the second order maxima of the two waves?

When light with a wavelength of 425 nm uniformly illuminates a single slit, the central bright fringe, observed on a screen located 0.630 m from the slit, has a width of 0.0166 m. What is the width of the slit?

Two stars are just barely resolved by a telescope with a lens diameter of 0.500 m. Determine the angular separation of the two stars. Assume incident light of wavelength 500.0 nm.

Light from a laser ( λ\lambdaλ = 640 nm) passes through a diffraction grating and spreads out into three beams as shown in the figure. Determine the spacing between the slits of the grating.

Light of wavelength 530 nm is incident on two slits that are spaced 1.0 mm apart. If each of the slits has a width of 0.10 mm, how many interference maxima lie within the central diffraction peak?

Two candles are lit and separated by 0.10 m. If the diameter of the pupil of an observer's eye is 3.5 mm, what is the maximum distance that the candles can be away from the observer and be seen as two light sources? Use 545 nm for the wavelength of light in the eye.

Visible light of wavelength 589 nm is incident on a diffraction grating that has 3500 lines/cm. At what angle with respect to the central maximum is the fifth order maximum observed?

A diffraction grating that has 4500 lines/cm is illuminated by light that has a single wavelength. If a second order maximum is observed at an angle of 42° with respect to the central maximum, what is the wavelength of this light?

White light is passed through a diffraction grating that has 2.50 × 105 lines/m. On each side of the white central maximum, a spectrum of colors is observed. What is the wavelength of the light observed at an angle of 7.00° in the first-order bright fringes?

A 30.0-mm wide diffraction grating produces a deviation of 30.0° in the second order principal maxima. The wavelength of light is 600.0 nm. What is the total number of slits on the grating?

The headlights of a car are 1.6 m apart and produce light of wavelength 575 nm in vacuum. The pupil of the eye of the observer has a diameter of 4.0 mm and a refractive index of 1.4. What is the maximum distance from the observer that the two headlights can be distinguished?

Which one of the following statements provides the most convincing evidence that electromagnetic waves have a transverse character?

The wavelength of light emitted from two distant objects is 715 nm. What is the minimum angle at which these objects can just be resolved when using binoculars with a 50-mm objective lens?

Red light of wavelength 600.0 nm is incident on a grating. If the separation between the slits is 5.0 × 10^-⁵ m, at what angle does the first principal maximum occur?

Light from two sources, $\lambda$ ₁ = 623 nm and $\lambda$ ₂ = 488 nm, is incident on a diffraction grating that has 5550 lines/cm. What is the angular separation, $\theta$ ₁ - $\theta$ ₂, of the second order maxima of the two waves?

White light is passed through a diffraction grating that has 2.50 × 10⁵ lines/m. On each side of the white central maximum, a spectrum of colors is observed. What is the wavelength of the light observed at an angle of 7.00° in the first-order bright fringes?