Question 1

A multiple-slit diffraction grating has a slit separation of 1.75 × 10−⁶ m.Find the wavelength of the monochromatic light that will have its second-order bright fringe diffracted through an angle of 36.0°.(1 nm = 10−⁹ m)

Accepted Answer

The formula for the angle of the bright fringe in a multiple-slit diffraction grating is given by:

sinθ = mλ/d

where m is the order of the bright fringe (in this case, m = 2 for the second-order bright fringe), λ is the wavelength of the light, d is the slit separation, and θ is the angle of the bright fringe.

We can rearrange this formula to solve for the wavelength:

λ = md/sinθ

Plugging in the given values, we get:

λ = (2)(1.75 × 10^-16 m)/(sin 36.0°)

Using a calculator, we find:

λ ≈ 514 nm

which corresponds to answer choice C.

Question 2

At what angle will the fourth-order maximum occur for a wavelength of 513 nm using a diffraction grating with 10 890 lines per cm?

Accepted Answer

The angle for a maximum in a diffraction grating is given by the equation $d\sin(\theta) = m\lambda$, where $d$ is the grating spacing, $m$ is the order of the maximum, and $\lambda$ is the wavelength. The grating spacing $d$ can be found from the number of lines per cm, which is $10,890$ lines/cm or $108,900$ lines/m, giving $d = \frac{1}{108,900}$ m. For the fourth-order maximum ($m=4$) and $\lambda = 513$ nm or $513 \times 10^{-9}$ m, substituting these values into the equation would result in $\sin(\theta)$ being greater than 1, which is impossible, indicating that a fourth-order maximum cannot occur with these parameters.

Question 3

At what angle will the highest-order maximum appear for a wavelength of 412 nm using a grating with 435 lines per mm?

Accepted Answer

We can use the formula for the angles of the maxima for a diffraction grating:

sinθ = mλ/d

where m is the order of the maximum, λ is the wavelength of the light, d is the spacing between the grooves in the grating, and θ is the angle of diffraction.

We can first find the spacing between the grooves:

d = 1/435 mm = 2.30 x 10^-3 mm

We want to find the angle for the highest-order maximum, which corresponds to m = 1 for a diffraction grating. Plugging in the values:

sinθ = (1)(412 nm)/(2.30 x 10^-3 mm)

sinθ = 0.998

Taking the inverse sine, we get:

θ = 81.3°

However, this is the angle for the first-order maximum. To find the angle for the highest-order maximum, we need to subtract the angle for the first-order maximum from 90°:

θ_max = 90° - θ_first

θ_max = 90° - 81.3°

θ_max = 8.7°

Therefore, the angle for the highest-order maximum is 8.7°, which corresponds to choice B.

Question 4

In the straight-ahead direction (θ = 0°)in Fraunhofer diffraction,which of the following is observed on the screen?

Accepted Answer

The answer of In the straight-ahead direction (θ = 0°)in...

Question 5

Sodium's emission lines at 589.0 nm and 589.6 nm pass through a diffraction grating and form two m = +1 maxima on a viewing screen.For which situation would the spacing between the two lines increase?​

Accepted Answer

The spacing between diffraction maxima is directly proportional to the order of the maxima (m). Viewing the maxima in second order (m=2) would increase the spacing between the two lines compared to first order (m=1).

Question 6

Diffraction grating №1 has half the lines/cm that diffraction grating №2 does.When used with a certain wavelength of light,both gratings give first-order maxima.Which of the following statements is true for the same wavelength of light.

Accepted Answer

The answer of Diffraction grating №1 has half the lines/cm...

Question 7

Helium-neon laser light (λ = 632.8 nm)is sent through a single slit of width 0.55 mm.What is the width of the central maximum on a screen 1.4 m in back of the slit? (1 nm = 10−⁹ m)

Accepted Answer

The width of the central maximum ($W$) in a single-slit diffraction pattern is given by the formula $W = 2L\lambda / a$, where $L$ is the distance from the slit to the screen (1.4 m), $\lambda$ is the wavelength of the light (632.8 nm = $632.8 \times 10^{-9}$ m), and $a$ is the width of the slit (0.55 mm = $0.55 \times 10^{-3}$ m). Substituting the given values, $W = 2 \times 1.4 \times (632.8 \times 10^{-9}) / (0.55 \times 10^{-3}) = 3.2 \times 10^{-3}$ m or 3.2E-3 m.

Question 8

In a single-slit diffraction experiment,the angular width of the central maximum is 0.16°.The width of the slit is then doubled as is the distance to the screen.What is the resulting angular width of the central maximum?

Accepted Answer

The angular width of the central maximum is given by: 
θ = λ/d
where λ is the wavelength of the light and d is the width of the slit.
When the slit width is doubled, the angular width of the central maximum becomes:
θ' = λ/2d
Similarly, when the distance to the screen is doubled, the angular width becomes:
θ'' = λ/4d
Since we are only doubling the slit width and distance, the wavelength of the light remains the same. Therefore, we can use the ratio of the new and old angular widths to find the answer:
θ''/θ = (λ/4d)/(λ/d) = 1/4
Therefore, the new angular width of the central maximum is:
θ'' = (1/4)θ = (1/4)(0.16°) = 0.04° = 0.080°
So the best choice is B.

Question 9

In a single-slit diffraction experiment,the width of the central maximum is 6.0 mm.The width of the slit is then doubled as is the distance to the screen.What is the resulting width of the central maximum?

Accepted Answer

The width of the central maximum is directly proportional to the width of the slit and inversely proportional to the distance to the screen. Doubling the width of the slit will double the width of the central maximum, but also doubling the distance to the screen will reduce the width by a factor of 2. Therefore, the resulting width of the central maximum will be the same as before, which is 6.0 mm.

Question 10

A diffraction grating has 6 700 lines/cm.What is the slit separation?

Accepted Answer

The slit separation can be found using the equation: d=1/N where d is the slit separation and N is the number of lines per unit length. Substituting the given values, we get: d=1/(6700 lines/cm x 100 cm/m) = 1.5 x 10^-6 m. Therefore, the correct answer is B.

Question 11

A beam of polarized light of intensity I₀ passes through a sheet of ideal polarizing material.The polarization axis of the beam and the transmission axis of the sheet differ by 38°.What is the intensity of the emerging light?

Accepted Answer

The intensity of the emerging light is given by Malus's Law: I = I₀ * cos²(θ), where θ is the angle between the light's polarization direction and the transmission axis. For θ = 38°, I = I₀ * cos²(38°) ≈ 0.62I₀.

Question 12

A wavelength of 540 nm yields a first-order maximum at 13.4° with a grating.At what angle will the second-order maximum appear for this wavelength?

Accepted Answer

We can use the grating equation:

n*λ = d*sin(θ)

where n is the order, λ is the wavelength, d is the grating spacing, and θ is the angle of diffraction.

For the first-order maximum:

1*540 nm = d*sin(13.4°)

Solving for d, we get:

d = 1.22 μm

Now, for the second-order maximum:

2*540 nm = d*sin(θ)

Solving for θ, we get:

θ = sin^(-1)((2*540 nm)/d)

Plugging in d = 1.22 μm, we get:

θ = 28°

Therefore, the second-order maximum appears at an angle of 28°. Choice (D) is the correct answer.

Question 13

A laser shines 630-nm light through a grating producing a first-order (m = 1)maximum at an angle of 30°.A second laser produces a first-order maximum with the same grating at 20°.What is the wavelength emitted by the second laser?

Accepted Answer

The grating equation is:d(sin θ_m + sin θ_i) = mλwhere d is the grating spacing, θ_m is the angle of the mth-order maximum, θ_i is the angle of incidence, and λ is the wavelength of light.For the first laser, we have:d(sin 30° + sin 0°) = 1(630 nm)d = 315 nmFor the second laser, we have:d(sin 20° + sin 0°) = 1(λ)λ = 431 nm

Question 14

A beam of unpolarized light in air strikes a flat piece of glass at an angle of incidence of 50.6°.If the reflected beam is completely polarized,what is the index of refraction of the glass?

Accepted Answer

The answer of A beam of unpolarized light in air...

Question 15

What is the highest-order (m value)maximum for wavelength 450 nm that can be obtained with a grating with 300 lines per mm?

Accepted Answer

The highest-order maximum (m value) can be calculated using the grating equation $d\sin(\theta) = m\lambda$, where $d$ is the grating spacing, $\lambda$ is the wavelength, and $m$ is the order of the maximum. The grating spacing $d$ is the inverse of the number of lines per mm, so for 300 lines per mm, $d = \frac{1}{300 \text{ mm}^{-1}} = \frac{1}{300000 \text{ m}^{-1}} = 3.33 \times 10^{-6} \text{ m}$. To find the highest possible order, we need the maximum value of $\sin(\theta)$, which is 1 (when $\theta = 90^\circ$). Thus, $m = \frac{d}{\lambda}$. Substituting the given values, $m = \frac{3.33 \times 10^{-6} \text{ m}}{450 \times 10^{-9} \text{ m}} = 7.4$. Since $m$ must be an integer, the highest possible order is 7.

Question 16

That all points on a wave front act as new sources of spherical waves is attributed to:

Accepted Answer

This idea is known as Huygens' principle or Huygens-Fresnel principle, which was proposed by Dutch physicist Christiaan Huygens in the 17th century.

Question 17

A diffraction grating with 11 800 lines/cm will exhibit the first-order maximum for light of wavelength 416 nm at what angle? (1 nm = 10−⁹ m)

Accepted Answer

The angle for the first-order maximum can be found using the formula d*sin(θ) = m*λ, where d is the distance between grating lines (1/11,800 cm), m is the order (1), and λ is the wavelength (416 nm). Converting units and solving gives θ ≈ 29.4°.

Question 18

What is the highest-order maximum for wavelength 454 nm that can be obtained with a grating with 375 lines per mm?

Accepted Answer

The answer of What is the highest-order maximum for wavelength...

Question 19

Polarization of light can be achieved using a dichroic material like Polaroid by which of the following processes?

Accepted Answer

Dichroic materials like Polaroid work based on the principle of selective absorption. These materials allow only light waves that vibrate in one direction (i.e., in one plane) to pass through and absorb all other vibrations. As a result, the transmitted light becomes polarized, with its electric field oscillating in a single plane. Reflection, double refraction, and scattering do not involve selective absorption and do not result in polarization.

Question 20

A Fraunhofer diffraction pattern is produced from a light source of wavelength 460 nm.The light goes through a single slit and onto a screen 0.9 m away.The first dark fringe is 4.5 mm from the central bright fringe.What is the slit width? (1 nm = 10−⁹ m)

Accepted Answer

The width of the slit ($a$) in a single-slit diffraction pattern can be calculated using the formula for the position of the first minimum ($y$) given by $y = \frac{\lambda L}{a}$, where $\lambda$ is the wavelength of the light, $L$ is the distance from the slit to the screen, and $y$ is the distance from the central maximum to the first minimum (dark fringe). Rearranging the formula to solve for $a$, we get $a = \frac{\lambda L}{y}$. Substituting the given values ($\lambda = 460 \times 10^{-9}$ m, $L = 0.9$ m, and $y = 4.5 \times 10^{-3}$ m), we find $a = \frac{460 \times 10^{-9} \times 0.9}{4.5 \times 10^{-3}} = 9.2 \times 10^{-5}$ m.

Quiz 24: Wave Optics

A multiple-slit diffraction grating has a slit separation of 1.75 × 10−⁶ m.Find the wavelength of the monochromatic light that will have its second-order bright fringe diffracted through an angle of 36.0°.(1 nm = 10−⁹ m)

At what angle will the fourth-order maximum occur for a wavelength of 513 nm using a diffraction grating with 10 890 lines per cm?

At what angle will the highest-order maximum appear for a wavelength of 412 nm using a grating with 435 lines per mm?

In the straight-ahead direction (θ = 0°) in Fraunhofer diffraction,which of the following is observed on the screen?

Sodium's emission lines at 589.0 nm and 589.6 nm pass through a diffraction grating and form two m = +1 maxima on a viewing screen.For which situation would the spacing between the two lines increase?

Diffraction grating №1 has half the lines/cm that diffraction grating №2 does.When used with a certain wavelength of light,both gratings give first-order maxima.Which of the following statements is true for the same wavelength of light.

Helium-neon laser light (λ = 632.8 nm) is sent through a single slit of width 0.55 mm.What is the width of the central maximum on a screen 1.4 m in back of the slit? (1 nm = 10−⁹ m)

In a single-slit diffraction experiment,the angular width of the central maximum is 0.16°.The width of the slit is then doubled as is the distance to the screen.What is the resulting angular width of the central maximum?

In a single-slit diffraction experiment,the width of the central maximum is 6.0 mm.The width of the slit is then doubled as is the distance to the screen.What is the resulting width of the central maximum?

A diffraction grating has 6 700 lines/cm.What is the slit separation?

A beam of polarized light of intensity I₀ passes through a sheet of ideal polarizing material.The polarization axis of the beam and the transmission axis of the sheet differ by 38°.What is the intensity of the emerging light?

A wavelength of 540 nm yields a first-order maximum at 13.4° with a grating.At what angle will the second-order maximum appear for this wavelength?

A laser shines 630-nm light through a grating producing a first-order (m = 1) maximum at an angle of 30°.A second laser produces a first-order maximum with the same grating at 20°.What is the wavelength emitted by the second laser?

A beam of unpolarized light in air strikes a flat piece of glass at an angle of incidence of 50.6°.If the reflected beam is completely polarized,what is the index of refraction of the glass?

What is the highest-order (m value) maximum for wavelength 450 nm that can be obtained with a grating with 300 lines per mm?

That all points on a wave front act as new sources of spherical waves is attributed to:

A diffraction grating with 11 800 lines/cm will exhibit the first-order maximum for light of wavelength 416 nm at what angle? (1 nm = 10−⁹ m)

What is the highest-order maximum for wavelength 454 nm that can be obtained with a grating with 375 lines per mm?

Polarization of light can be achieved using a dichroic material like Polaroid by which of the following processes?

A Fraunhofer diffraction pattern is produced from a light source of wavelength 460 nm.The light goes through a single slit and onto a screen 0.9 m away.The first dark fringe is 4.5 mm from the central bright fringe.What is the slit width? (1 nm = 10−⁹ m)

Quiz 24: Wave Optics

A multiple-slit diffraction grating has a slit separation of 1.75 × 10−6 m.Find the wavelength of the monochromatic light that will have its second-order bright fringe diffracted through an angle of 36.0°.(1 nm = 10−9 m)

At what angle will the fourth-order maximum occur for a wavelength of 513 nm using a diffraction grating with 10 890 lines per cm?

At what angle will the highest-order maximum appear for a wavelength of 412 nm using a grating with 435 lines per mm?

In the straight-ahead direction (θ = 0°) in Fraunhofer diffraction,which of the following is observed on the screen?

Sodium's emission lines at 589.0 nm and 589.6 nm pass through a diffraction grating and form two m = +1 maxima on a viewing screen.For which situation would the spacing between the two lines increase?​

Diffraction grating №1 has half the lines/cm that diffraction grating №2 does.When used with a certain wavelength of light,both gratings give first-order maxima.Which of the following statements is true for the same wavelength of light.

Helium-neon laser light (λ = 632.8 nm) is sent through a single slit of width 0.55 mm.What is the width of the central maximum on a screen 1.4 m in back of the slit? (1 nm = 10−9 m)

In a single-slit diffraction experiment,the angular width of the central maximum is 0.16°.The width of the slit is then doubled as is the distance to the screen.What is the resulting angular width of the central maximum?

In a single-slit diffraction experiment,the width of the central maximum is 6.0 mm.The width of the slit is then doubled as is the distance to the screen.What is the resulting width of the central maximum?

A diffraction grating has 6 700 lines/cm.What is the slit separation?

A beam of polarized light of intensity I0 passes through a sheet of ideal polarizing material.The polarization axis of the beam and the transmission axis of the sheet differ by 38°.What is the intensity of the emerging light?

A wavelength of 540 nm yields a first-order maximum at 13.4° with a grating.At what angle will the second-order maximum appear for this wavelength?

A laser shines 630-nm light through a grating producing a first-order (m = 1) maximum at an angle of 30°.A second laser produces a first-order maximum with the same grating at 20°.What is the wavelength emitted by the second laser?

A beam of unpolarized light in air strikes a flat piece of glass at an angle of incidence of 50.6°.If the reflected beam is completely polarized,what is the index of refraction of the glass?

What is the highest-order (m value) maximum for wavelength 450 nm that can be obtained with a grating with 300 lines per mm?

That all points on a wave front act as new sources of spherical waves is attributed to:

A diffraction grating with 11 800 lines/cm will exhibit the first-order maximum for light of wavelength 416 nm at what angle? (1 nm = 10−9 m)

What is the highest-order maximum for wavelength 454 nm that can be obtained with a grating with 375 lines per mm?

Polarization of light can be achieved using a dichroic material like Polaroid by which of the following processes?

A Fraunhofer diffraction pattern is produced from a light source of wavelength 460 nm.The light goes through a single slit and onto a screen 0.9 m away.The first dark fringe is 4.5 mm from the central bright fringe.What is the slit width? (1 nm = 10−9 m)

A multiple-slit diffraction grating has a slit separation of 1.75 × 10−⁶ m.Find the wavelength of the monochromatic light that will have its second-order bright fringe diffracted through an angle of 36.0°.(1 nm = 10−⁹ m)

Sodium's emission lines at 589.0 nm and 589.6 nm pass through a diffraction grating and form two m = +1 maxima on a viewing screen.For which situation would the spacing between the two lines increase?

Helium-neon laser light (λ = 632.8 nm) is sent through a single slit of width 0.55 mm.What is the width of the central maximum on a screen 1.4 m in back of the slit? (1 nm = 10−⁹ m)

A beam of polarized light of intensity I₀ passes through a sheet of ideal polarizing material.The polarization axis of the beam and the transmission axis of the sheet differ by 38°.What is the intensity of the emerging light?

A diffraction grating with 11 800 lines/cm will exhibit the first-order maximum for light of wavelength 416 nm at what angle? (1 nm = 10−⁹ m)

A Fraunhofer diffraction pattern is produced from a light source of wavelength 460 nm.The light goes through a single slit and onto a screen 0.9 m away.The first dark fringe is 4.5 mm from the central bright fringe.What is the slit width? (1 nm = 10−⁹ m)