Question 1

A beam of monochromatic light passes through a slit that is 11.0 μm wide.If the first order dark fringe of the resulting diffraction pattern is at an angle of 4.31° away from the centerline,what is the wavelength of light?
A)827 nm
B)301 nm
C)602 nm
D)402 nm
E)201 nm

Accepted Answer

The wavelength of light can be calculated using the formula for the first minimum in a single-slit diffraction pattern, which is $\lambda = a \sin(\theta)$, where $a$ is the slit width and $\theta$ is the angle to the first dark fringe. Given $a = 11.0 \mu m = 11.0 \times 10^{-6} m$ and $\theta = 4.31^\circ$, converting $\theta$ to radians gives $\theta = 4.31 \times (\pi/180)$. Substituting these values into the formula yields $\lambda \approx 827 nm$.

Question 2

When a diffraction grating having 5000 lines/cmis illuminated by monochromatic light,the angle between the central maximum and the fourth order maximum is 47.2°.What is the wavelength of the light?
A)138 nm
B)183 nm
C)367 nm
D)637 nm

Accepted Answer

We can use the formula for diffraction grating to find the wavelength of the light:

mλ = d sinθ

where m is the order of the maximum, λ is the wavelength of the light, d is the distance between the grating lines (d = 1/5000 cm), and θ is the angle between the central maximum and the mth maximum.

For the fourth order maximum, m = 4 and θ = 47.2°. Substituting these values into the formula, we get:

4λ = (1/5000) sin 47.2°

Solving for λ, we get:

λ = (1/5000) sin 47.2°/4

λ ≈ 367 nm

Question 3

A beam of light of wavelength 630 nm is incident on a slit that is 0.400 mm wide.If the distance between the slit and the screen is 1.80 m,what is the width on the screen of the central bright fringe?
A)1.94 mm
B)2.94 mm
C)3.54 mm
D)5.67 mm
E)6.94 mm

Accepted Answer

The answer of A beam of light of wavelength 630...

Question 4

A diffraction grating has 6.00 × 10³ 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? A)20.5° B)30.5° C)40.6° D)50.5°

Accepted Answer

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Question 5

When light illuminates a diffraction grating with 7000 lines per centimeter,its second order maximum is at 62.4°.What is the wavelength of the light?
A)336 nm
B)363 nm
C)633 nm
D)752 nm

Accepted Answer

The diffraction grating equation is given by:

mλ = d sinθ

where m is the order of the maximum, λ is the wavelength of light, d is the distance between adjacent slits in the grating, and θ is the angle between the incident light and the direction of the maximum.

Here, we are given that the grating has 7000 lines per centimeter, which means that the distance between adjacent slits is:

d = 1/7000 cm = 1.43 × 10^-4 cm

We are also given that the maximum is at the second order (m = 2) and at an angle of θ = 62.4°.

Substituting these values into the diffraction grating equation, we get:

2λ = (1.43 × 10^-4 cm) sin62.4°

Simplifying and solving for λ, we get:

λ = (1.43 × 10^-4 cm) sin62.4° / 2

λ ≈ 633 nm

Therefore, the best choice is C, with a wavelength of 633 nm.

Question 6

Monochromatic light is incident on a diffraction 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)202 nm
B)403 nm
C)605 nm
D)806 nm

Accepted Answer

The wavelength ($\lambda$) can be calculated using the diffraction grating equation $d\sin\theta = m\lambda$, where $d$ is the grating spacing, $\theta$ is the diffraction angle, and $m$ is the order of the maximum. Given that the grating is 75 mm wide with 50,000 lines, the spacing $d = \frac{75 mm}{50,000} = 1.5 \times 10^{-3} mm = 1.5 \times 10^{-6} m$. For the second-order maximum ($m = 2$) at $\theta = 32.5°$, solving for $\lambda$ gives $\lambda = \frac{d\sin\theta}{m} = \frac{1.5 \times 10^{-6} \sin(32.5°)}{2} \approx 403 nm$.

Question 7

A diffraction grating with 396 lines/mm is illuminated with light of wavelength 343 nm.What is the angular separation between the two second-order bright fringes?
A)31.5°
B)15.8°
C)32.9°

Accepted Answer

The angular separation between the two second-order bright fringes is given by:$$	heta = \sin^{-1}\left(\frac{m\lambda}{d}ight)$$where:* m is the order of the bright fringe (m = 2)* λ is the wavelength of light (λ = 343 nm)* d is the distance between the lines on the grating (d = 1/396 mm)Plugging in these values, we get:$$	heta = \sin^{-1}\left(\frac{2 	imes 343 	imes 10^{-9} 	ext{ m}}{1/396 	imes 10^{-3} 	ext{ m}}ight) = 31.5^\circ$$

Question 8

An 18-mm-wide diffraction grating has rulings of 710 lines per millimeter.Monochromatic light of wavelength 506 nm wavelength is incident normally on the grating.What is the largest angle from the centerline at which an intensity maximum is formed?
A)46°
B)44°
C)42°
D)40°
E)38°

Accepted Answer

The diffraction angle θ for maximum intensity is given by the grating equation: d*sin(θ) = m*λ, where d is the distance between lines (1/710 mm), λ is the wavelength (506 nm), and m is the order number. The largest angle occurs at the highest possible m where sin(θ) ≤ 1. Calculating for m = 25 gives θ ≈ 46°.

Question 9

When light of wavelength 450 nm falls on a single slit of width 0.30 mm,what is the angular width of the central bright region?
A)0.086°
B)0.13°
C)0.17°
D)0.26°
E)0.35°

Accepted Answer

The answer of When light of wavelength 450 nm falls...

Question 10

Light of wavelength 610 nm is incident on a slit 0.20 mm wide and the diffraction pattern is viewed on a screen that is 1.5 m from the slit.What is the width on the screen of the central maximum?
A)0.34 cm
B)0.68 cm
C)0.92 cm
D)1.2 cm
E)1.5 cm

Accepted Answer

The answer of Light of wavelength 610 nm is incident...

Question 11

A beam of light of wavelength 610 nm passes through a slit that is 1.90 µm wide.At what the angle away from the centerline does the first dark fringe occur?
A)9.35°
B)11.4°
C)12.2°
D)39.9°
E)18.7°

Accepted Answer

The answer of A beam of light of wavelength 610...

Question 12

Light of wavelength 687 nm passes through a single slit that is 0.75 mm wide.At what distance from the slit should a screen be placed so that the second dark fringe in the diffraction pattern is to be 1.7 mm from the center of the pattern?
A)0.39 m
B)0.93 m
C)1.1 m
D)1.5 m
E)1.9 m

Accepted Answer

The position of the dark fringes in a single-slit diffraction pattern can be calculated using the formula $y = \frac{m\lambda L}{a}$, where $y$ is the distance from the center of the pattern to the m-th dark fringe, $\lambda$ is the wavelength of the light, $L$ is the distance from the slit to the screen, $a$ is the width of the slit, and $m$ is the order number of the dark fringe. For the second dark fringe, $m = 2$, $\lambda = 687 \times 10^{-9}$ m (687 nm converted to meters), $a = 0.75 \times 10^{-3}$ m (0.75 mm converted to meters), and $y = 1.7 \times 10^{-3}$ m (1.7 mm converted to meters). Rearranging the formula to solve for $L$, we get $L = \frac{ya}{m\lambda}$. Plugging in the values, $L = \frac{(1.7 \times 10^{-3})(0.75 \times 10^{-3})}{2(687 \times 10^{-9})} \approx 0.93$ meters.

Question 13

When a single slit that is 0.050 mm wide is illuminated by light of 550-nm wavelength,what is the angular separation between the first two minima on one side of the central maximum?
A)0.36°
B)0.47°
C)0.54°
D)0.63°
E)1.3°

Accepted Answer

The angular position of the minima in a single-slit diffraction pattern is given by the formula θ = mλ/a, where m is the order of the minimum, λ is the wavelength, and a is the slit width. For the first two minima (m=1 and m=2), the angular separation is (2λ/a) - (λ/a) = λ/a. Substituting the given values, θ = (550 x 10^-9 m) / (0.050 x 10^-3 m) = 0.011 radians, which is approximately 0.63°.

Question 14

Monochromatic light of wavelength 500 nm is incident normally on a diffraction grating.If the third-order maximum of the diffraction pattern is observed at 32.0°,what is the total number of maxima can be seen?
A)5
B)7
C)10
D)11
E)8

Accepted Answer

The total number of maxima is given by (m+1), where m is the order of the maximum. In this case, the third-order maximum is observed, so the total number of maxima is (3+1) = 4.

Question 15

A beam of light of wavelength 610 nm passes through a slit that is 1.90 µm wide.At what the angle away from the centerline does the second dark fringe occur?
A)11.4°
B)9.35°
C)12.2°
D)39.9°
E)18.7°

Accepted Answer

The answer of A beam of light of wavelength 610...

Question 16

What is the angular separation of two spectral lines of wavelengths 497 nm and 251 nm formed in the third order with a diffracting grating having 587 lines per millimeter?
A)34.8°
B)24.8°
C)41.3°
D)29.4°
E)4.21°

Accepted Answer

Explanation:The angular separation between two spectral lines of wavelengths λ1 and λ2 formed in the nth order with a diffracting grating having N lines per millimeter is given by:θ = sin^-1[(nλ2 - nλ1)/d]where d is the grating spacing (1/N).Substituting the given values, we get:θ = sin^-1[(3 x 251 nm - 3 x 497 nm)/(1/587 mm)]= sin^-1(-0.00069)= 34.8°Therefore, the correct choice is A.

Question 17

A single thin slit forms a diffraction pattern when illuminated with monochromatic light.The fourth minimum of the pattern occurs at an angle of 32.0° away from the central maximum.At what angle does the fifth minimum occur?
A)41.5°
B)41.0°
C)40.5°
D)42.0°
E)42.5°

Accepted Answer

The angle for the minima in a single slit diffraction pattern is given by $\sin(\theta) = \frac{m\lambda}{a}$, where $m$ is the order of the minimum, $\lambda$ is the wavelength of the light, and $a$ is the width of the slit. For two different minima, $m_1$ and $m_2$, with angles $\theta_1$ and $\theta_2$, the equation can be set up for each and then divided to eliminate $\lambda/a$, giving $\frac{\sin(\theta_1)}{m_1} = \frac{\sin(\theta_2)}{m_2}$. Given the fourth minimum occurs at 32.0°, we can find the angle for the fifth minimum by setting $m_1 = 4$, $\theta_1 = 32.0°$, and $m_2 = 5$, and solving for $\theta_2$. This approach leads to the calculation of the angle for the fifth minimum, which is approximately 41.5°, option A.

Question 18

Light of wavelength 580 nm is incident on a slit of width 0.30 mm.An observing screen is placed 2.0 m past the slit.Find the distance on the screen of the first order dark fringe from the center of the pattern.
A)0.26 mm
B)1.5 mm
C)1.9 mm
D)3.9 mm
E)7.7 mm

Accepted Answer

The answer of Light of wavelength 580 nm is incident...

Question 19

A beam of light of wavelength 600 nm passes through a slit that is 3.1 × 10^-5 m wide,and then goes on to a screen that is 2.2 m from the slit.On the screen,how far is the second dark fringe from the center of the diffraction pattern? A)3.9 cm B)4.2 cm C)6.3 cm D)2.1 cm E)8.5 cm

Accepted Answer

The answer of A beam of light of wavelength 600...

Question 20

Monochromatic light of wavelength 500 nm is incident normally on a diffraction grating.If the third-order maximum of the diffraction pattern is observed at 32° from the centerline,what is the distance between the slits of the grating?
A)0.93 μm
B)1.4 μm
C)2.8 μm
D)8.5 μm

Accepted Answer

We can use the formula for diffraction grating to solve this problem:

d*sin(θ) = mλ

Where d is the distance between the slits, θ is the angle of diffraction for a particular order (measured from the centerline), m is the order of the maximum, and λ is the wavelength of the light.

Here, we are given λ = 500 nm, θ = 32°, and m = 3. Solving for d, we get:

d = mλ/sin(θ)

d = 3*500 nm / sin(32°)

d = 2.8 μm

Therefore, the distance between the slits of the grating is 2.8 μm, which is option C.

Quiz 28: Physical Optics: Interference and Diffraction

A beam of monochromatic light passes through a slit that is 11.0 μm wide.If the first order dark fringe of the resulting diffraction pattern is at an angle of 4.31° away from the centerline,what is the wavelength of light?

When a diffraction grating having 5000 lines/cmis illuminated by monochromatic light,the angle between the central maximum and the fourth order maximum is 47.2°.What is the wavelength of the light?

A beam of light of wavelength 630 nm is incident on a slit that is 0.400 mm wide.If the distance between the slit and the screen is 1.80 m,what is the width on the screen of the central bright fringe?

A diffraction grating has 6.00 × 103 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 diffraction grating with 7000 lines per centimeter,its second order maximum is at 62.4°.What is the wavelength of the light?

Monochromatic light is incident on a diffraction 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 diffraction grating with 396 lines/mm is illuminated with light of wavelength 343 nm.What is the angular separation between the two second-order bright fringes?

An 18-mm-wide diffraction grating has rulings of 710 lines per millimeter.Monochromatic light of wavelength 506 nm wavelength is incident normally on the grating.What is the largest angle from the centerline at which an intensity maximum is formed?

When light of wavelength 450 nm falls on a single slit of width 0.30 mm,what is the angular width of the central bright region?

Light of wavelength 610 nm is incident on a slit 0.20 mm wide and the diffraction pattern is viewed on a screen that is 1.5 m from the slit.What is the width on the screen of the central maximum?

A beam of light of wavelength 610 nm passes through a slit that is 1.90 µm wide.At what the angle away from the centerline does the first dark fringe occur?

Light of wavelength 687 nm passes through a single slit that is 0.75 mm wide.At what distance from the slit should a screen be placed so that the second dark fringe in the diffraction pattern is to be 1.7 mm from the center of the pattern?

When a single slit that is 0.050 mm wide is illuminated by light of 550-nm wavelength,what is the angular separation between the first two minima on one side of the central maximum?

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

A beam of light of wavelength 610 nm passes through a slit that is 1.90 µm wide.At what the angle away from the centerline does the second dark fringe occur?

What is the angular separation of two spectral lines of wavelengths 497 nm and 251 nm formed in the third order with a diffracting grating having 587 lines per millimeter?

A single thin slit forms a diffraction pattern when illuminated with monochromatic light.The fourth minimum of the pattern occurs at an angle of 32.0° away from the central maximum.At what angle does the fifth minimum occur?

Light of wavelength 580 nm is incident on a slit of width 0.30 mm.An observing screen is placed 2.0 m past the slit.Find the distance on the screen of the first order dark fringe from the center of the pattern.

A beam of light of wavelength 600 nm passes through a slit that is 3.1 × 10-5 m wide,and then goes on to a screen that is 2.2 m from the slit.On the screen,how far is the second dark fringe from the center of the diffraction pattern?

Monochromatic light of wavelength 500 nm is incident normally on a diffraction grating.If the third-order maximum of the diffraction pattern is observed at 32° from the centerline,what is the distance between the slits of the grating?

A diffraction grating has 6.00 × 10³ 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?

A beam of light of wavelength 600 nm passes through a slit that is 3.1 × 10^-5 m wide,and then goes on to a screen that is 2.2 m from the slit.On the screen,how far is the second dark fringe from the center of the diffraction pattern?