Question 1

An 18-mm wide diffraction grating has rulings of 880 lines per mm.Monochromatic light of 590 nm wavelength is incident normally on the grating.What is the largest angle,measured from the central bright spot,at which an intensity maximum is formed?
A) 31°
B) 29°
C) 27°
D) 25°
E) 23°

Accepted Answer

The diffraction angle can be found using the grating equation: d*sin(θ) = m*λ, where d is the distance between lines (1/880 mm), λ is the wavelength (590 nm), and m is the order of the maximum. The largest angle occurs at the highest possible m where sin(θ) ≤ 1. Calculating for m = 3 gives the largest angle of approximately 31°.

Question 2

A diffraction grating has 450 lines per mm.What is the highest order m that contains the entire visible spectrum from 400 nm to 700 nm?
A) m = 2
B) m = 3
C) m = 4
D) m = 5
E) m = 6

Accepted Answer

The highest order m that contains the entire visible spectrum is given by the formula nλ = d sinθ for bright spots, where n is the order, λ is the wavelength of light, d is the spacing between the grating lines, and θ is the angle of diffraction. Since we want the entire visible spectrum to diffract, we need to find the angle θ that will result in the longest wavelength (700 nm) being diffracted at the edge of the spectrum. Using the formula θ = sin^-1(nλ/d), we can solve for n when θ is equal to the inverse sine of 700 nm and d is equal to 1/450 mm. We get n = 3.03, which means that the third order (m=3) diffraction maxima will contain the entire visible spectrum.

Question 3

A metallic sheet has a large number of slits,5.0 mm wide and 20 cm apart,and is used as a diffraction grating for microwaves.A wide parallel beam of microwaves is incident normally on the sheet.If the microwave wavelength is 6.0 cm,what is the largest angle away from the central maximum at which an intensity maximum occurs.
A) 64°
B) 69°
C) 74°
D) 79°
E) 84°

Accepted Answer

The largest angle away from the central maximum at which an intensity maximum occurs is given by:sin θ = mλ/dwhere m is the order of the maximum, λ is the wavelength, and d is the slit spacing.For the first-order maximum (m = 1), we have:sin θ = λ/d = 6.0 cm / 5.0 mm = 1.2θ = sin^-1(1.2) = 69°

Question 4

A diffraction grating is to be used to find the wavelength of the light in the emission spectrum of a gas.The grating spacing is not known,but a light having a known wavelength of 632.8 nm is deflected by 43.2° away from the central maximum in the second order by this grating.Light of the wavelength to be measured is deflected by 48.2° away from the central maximum in the second order.What is the wavelength of this light?

Accepted Answer

The answer of A diffraction grating is to be used...

Question 5

A diffraction grating has rulings of 890 lines/mm.When white light is incident normally on the grating,what is the longest wavelength that forms an intensity maximum in the fifth order?
A) 225 nm
B) 200 nm
C) 250 nm
D) 275 nm
E) 300 nm

Accepted Answer

The longest wavelength that forms an intensity maximum in the fifth order is given by:$$\lambda = \frac{d}{5m}$$where d is the grating spacing and m is the order of the maximum.Substituting the given values, we get:$$\lambda = \frac{1}{890 	ext{ lines/mm} 	imes 5} = 225 	ext{ nm}$$Therefore, the correct choice is A.

Question 6

A researcher is investigating a cubic crystal with X-rays.He is looking at Bragg reflection from the planes parallel to the cube faces.He finds that when using X-rays of 0.165 nm a strong first maximum occurs when the beam makes an angle of 23.5° with the planes.What is the spacing of adjacent atoms in the crystal?

Accepted Answer

The answer of A researcher is investigating a cubic crystal...

Question 7

A metallic sheet has a large number of slits,5.0 mm wide and 20 cm apart,and is used as a diffraction grating for microwaves.A wide parallel beam of microwaves is incident normally on the sheet.What is the smallest microwave frequency for which only the central maximum occurs? (c = 3.00 × 10⁸ m/s) A) 0.50 GHz B) 0.70 GHz C) 1.0 GHz D) 1.5 GHz E) 2.0 GHz

Accepted Answer

The answer of A metallic sheet has a large number...

Question 8

If an X-ray beam of wavelength 1.4 × 10^-10 m makes an angle of 20° with a set of planes in a crystal causing first order constructive interference,at what angle will the second order line appear? A) 40° B) 20° C) 43° D) 4.0° E) 11°

Accepted Answer

The Bragg's law states that constructive interference occurs when 2dsinθ = nλ, where d is the distance between the planes, θ is the angle of incidence, λ is the wavelength of the X-ray, and n is the order of the diffraction.

For the first order, n = 1, we have:

2dsin20° = 1.4 × 10^-10 m

d = 2.56 × 10^-10 m

For the second order, n = 2, we have:

2dsinθ = 2λ

2dsinθ = 2(1.4 × 10^-10 m)

sinθ = λ/d

sinθ = 2λ/2d

sinθ = λ/(2d/n)

sinθ = λ/(2(2.56 × 10^-10 m)/2)

sinθ = 1.4 × 10^-10 m/(2.56 × 10^-10 m)

θ = 43°

Therefore, the second order line will appear at an angle of 43°. The answer is C.

Question 9

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° from the central spot,how many TOTAL number of maxima can be seen?
A) 5
B) 7
C) 10
D) 11
E) 13

Accepted Answer

The angular position $	heta_m$ of the maxima is given by the equation:

$$d\sin(	heta_m)=m\lambda$$

where $d$ is the grating spacing, $\lambda$ is the wavelength, and $m$ is the order of the maximum.

For the third-order maximum, we have:

$$d\sin(	heta_3)=3\lambda$$

Since we know the wavelength and the angle, we can solve for the grating spacing:

$$d=\frac{3\lambda}{\sin(	heta_3)}=\frac{3(500\ \mathrm{nm})}{\sin(32.0^\circ)}\approx1130\ \mathrm{nm}$$

The total number of maxima that can be seen is given by:

$$N=\frac{L}{d}+1$$

where $L$ is the length of the grating (which we can assume to be infinite). Plugging in the values, we get:

$$N=\frac{\infty}{1130\ \mathrm{nm}}+1=\infty$$

But in practice, the number of maxima that can be seen is limited by the resolving power of the human eye and the intensity of the diffracted light. Typically, we can see up to about 10-20 maxima. Therefore, the closest answer choice is D) 11.

Question 10

A thin beam of laser light of wavelength 514 nm passes through a diffraction grating having 3952 lines/cm.The resulting pattern is viewed on a distant curved screen that can show all bright fringes up to and including ±90.0° from the central spot.If the experiment were performed with all of the apparatus under water (which has an index of refraction of 1.33),what would be the TOTAL number of bright spots that would show up on the screen?
A) 6
B) 7
C) 12
D) 13
E) 14

Accepted Answer

The number of bright spots in a diffraction grating can be calculated using the formula:

nλ = d sinθ

where n is the order of the bright spot (n=1,2,3...), λ is the wavelength of the light, d is the spacing between the lines in the grating, and θ is the angle between the central bright spot and the nth bright spot.

First, we need to calculate the spacing between the lines in the grating:

d = 1/3952 cm = 2.527 x 10^-4 cm

Next, we need to find the maximum angle at which we can see bright spots:

sinθ = 90°
θ = sin^-1(1) = 90°

Now we can calculate the maximum order of the bright spot that we can see:

nλ = d sinθ
n = d sinθ / λ
n = (2.527 x 10^-4 cm)(sin 90°) / (514 nm)
n = 0.000491

However, we need to take into account the refractive index of water. The wavelength of the light in water will be:

λwater = λ / nwater
λwater = 514 nm / 1.33
λwater = 386.5 nm

Now we can recalculate the maximum order of the bright spot:

nλwater = d sinθ
n = d sinθ / λwater
n = (2.527 x 10^-4 cm)(sin 90°) / (386.5 nm)
n = 0.000635

The maximum order of the bright spot that we can see is now 0.000635. We need to round up to the nearest whole number, so the maximum order is 1.

The total number of bright spots is given by:

# of bright spots = (2n + 1)^2
# of bright spots = (2(1) + 1)^2
# of bright spots = 9

However, we need to subtract the central bright spot, so the total number of bright spots that we will see on the screen is:

# of bright spots = 9 - 1
# of bright spots = 8

But we need to take into account that we can see bright fringes up to and including ±90.0° from the central spot. This means that we need to count both positive and negative orders of bright spots. So we double our result:

# of bright spots = 8 x 2
# of bright spots = 16

However, we need to subtract the central bright spot twice (once for positive orders and once for negative orders), so the final answer is:

# of bright spots = 16 - 2
# of bright spots = 14

Therefore, the answer is (D) 14.

Question 11

A diffraction grating has 300 lines per mm.If light of frequency 4.76 × 10¹⁴ Hz is sent through this grating,at what angle does the first order maximum occur? A) 56° B) 44° C) 22° D) 11° E) 28°

Accepted Answer

The answer of A diffraction grating has 300 lines per...

Question 12

In a diffraction grating 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?
A) 479 nm
B) 497 nm
C) 567 nm
D) 749 nm
E) 794 nm

Accepted Answer

We can use the formula for the diffraction grating:

dsinθ = mλ

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

For the first source:

d = unknown
θ = sin^-1(0.350/1) = 20.41°
m = 1
λ = 600 nm

Using the formula, we can solve for d:

d = (mλ) / sinθ = (1 x 600 x 10^-9) / sin(20.41°) = 1.09 x 10^-5 m

For the second source:

d = same as above
θ = sin^-1(0.870/3) = 18.93°
m = 3

Using the formula, we can solve for λ:

λ = (m sinθ) / d = (3 x sin(18.93°)) / (1.09 x 10^-5) = 4.97 x 10^-7 m = 497 nm

Therefore, the wavelength of the light from the second source is 497 nm, which corresponds to answer choice B.

Question 13

A He-Ne laser,which produces light of wavelength 632.8 nm,is used to calibrate a diffraction grating.If the first-order maximum occurs at 20.5° from the central spot,what is the distance between the slits of the grating?
A) 0.905 µm
B) 1.81 µm
C) 2.20 µm
D) 3.62 µm
E) 4.52 µm

Accepted Answer

The distance between the slits of the grating can be calculated using the equation:

d sinθ = mλ

where d is the distance between the slits, θ is the angle between the central spot and the first-order maximum, m is the order of the maximum (m=1 for first-order), and λ is the wavelength of the light.

Plugging in the given values, we get:

d sin(20.5°) = 1(632.8 nm)

Solving for d, we get:

d = 1(632.8 nm) / sin(20.5°) = 1.81 µm

Therefore, the correct answer is B.

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?
A) 8
B) 2
C) 6
D) 5
E) 5.3

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

A thin beam of laser light of wavelength 514 nm passes through a diffraction grating having 3952 lines/cm.The resulting pattern is viewed on a distant curved screen that can show all bright fringes up to and including ±90.0° from the central spot.What is the TOTAL number of bright fringes that will show up on the screen?
A) 4
B) 5
C) 8
D) 9
E) 10

Accepted Answer

The total number of bright fringes is given by 2N+1, where N is the number of lines per centimeter. In this case, N = 3952 lines/cm, so the total number of bright fringes is 2(3952) + 1 = 7905.

Question 16

Certain planes of a crystal of halite have a spacing of 0.399 nm.The crystal is irradiated by a beam of X-rays.First order constructive interference occurs when the beam makes an angle of 20° with the planes.What is the wavelength of the X-rays?
A) 0.14 nm
B) 0.17 nm
C) 0.21 nm
D) 0.24 nm
E) 0.27 nm

Accepted Answer

The answer of Certain planes of a crystal of halite...

Question 17

What is the angular separation of the two second-order spectral lines having wavelengths  and  using a diffraction grating having 456 lines/mm?
A) 1.63°
B) 1.52°
C) 0.815°
D) 3.26°

Accepted Answer

The answer of What is the angular separation of the...

Question 18

If an X-ray beam of wavelength 1.4 × 10^-10 m makes an angle of 30° with a set of planes in a crystal causing first order constructive interference,what is the plane spacing? A) 0.28 nm B) 0.070 nm C) 0.32 nm D) 0.16 nm E) 0.14 nm

Accepted Answer

Using Bragg's Law, nλ = 2d sin θ, for first order (n=1), λ = 1.4 × 10^-10 m, θ = 30°, solve for d: d = λ / (2 sin θ) = 1.4 × 10^-10 m / (2 × 0.5) = 1.4 × 10^-10 m = 0.14 nm.

Question 19

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) 202 nm
B) 403 nm
C) 452 nm
D) 605 nm
E) 806 nm

Accepted Answer

The wavelength ($\lambda$) can be calculated using the grating equation for diffraction maxima, $\lambda = \frac{d \sin \theta}{m}$, where $d$ is the grating spacing (the distance between adjacent lines), $\theta$ is the diffraction angle, and $m$ is the order of the maximum. Given that the grating is 75 mm wide and has 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 $32.5°$, $\lambda = \frac{1.5 \times 10^{-6} m \times \sin(32.5°)}{2}$. Calculating this gives a wavelength close to 403 nm.

Question 20

When monochromatic light illuminates a 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) 452 nm
D) 633 nm
E) 752 nm

Accepted Answer

The formula for finding the angle of diffraction for a grating is:
sinθ = mλ/d
Where:
θ = angle of diffraction
m = order of diffraction (in this case, m = 2)
λ = wavelength of light
d = distance between adjacent slits on the grating (in this case, d = 1/7000 cm)

Rearranging the formula to solve for λ, we get:
λ = d sinθ /m

Plugging in the known values:
d = 1/7000 cm
m = 2
sinθ = sin(62.4°)

λ = (1/7000 cm) x sin(62.4°)/2 = 6.33 x 10^-7 cm

Converting to nm:
λ = 633 nm

Therefore, the wavelength of the light is 633 nm, which corresponds to answer choice D.

Quiz 36: Diffraction

An 18-mm wide diffraction grating has rulings of 880 lines per mm.Monochromatic light of 590 nm wavelength is incident normally on the grating.What is the largest angle,measured from the central bright spot,at which an intensity maximum is formed?

A diffraction grating has 450 lines per mm.What is the highest order m that contains the entire visible spectrum from 400 nm to 700 nm?

A diffraction grating has rulings of 890 lines/mm.When white light is incident normally on the grating,what is the longest wavelength that forms an intensity maximum in the fifth order?

A metallic sheet has a large number of slits,5.0 mm wide and 20 cm apart,and is used as a diffraction grating for microwaves.A wide parallel beam of microwaves is incident normally on the sheet.What is the smallest microwave frequency for which only the central maximum occurs? (c = 3.00 × 108 m/s)

If an X-ray beam of wavelength 1.4 × 10-10 m makes an angle of 20° with a set of planes in a crystal causing first order constructive interference,at what angle will the second order line appear?

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° from the central spot,how many TOTAL number of maxima can be seen?

A diffraction grating has 300 lines per mm.If light of frequency 4.76 × 1014 Hz is sent through this grating,at what angle does the first order maximum occur?

A He-Ne laser,which produces light of wavelength 632.8 nm,is used to calibrate a diffraction grating.If the first-order maximum occurs at 20.5° from the central spot,what is the distance between the slits of the grating?

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?

Certain planes of a crystal of halite have a spacing of 0.399 nm.The crystal is irradiated by a beam of X-rays.First order constructive interference occurs when the beam makes an angle of 20° with the planes.What is the wavelength of the X-rays?

What is the angular separation of the two second-order spectral lines having wavelengths and using a diffraction grating having 456 lines/mm?

If an X-ray beam of wavelength 1.4 × 10-10 m makes an angle of 30° with a set of planes in a crystal causing first order constructive interference,what is the plane spacing?

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?

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

If an X-ray beam of wavelength 1.4 × 10^-10 m makes an angle of 20° with a set of planes in a crystal causing first order constructive interference,at what angle will the second order line appear?

If an X-ray beam of wavelength 1.4 × 10^-10 m makes an angle of 30° with a set of planes in a crystal causing first order constructive interference,what is the plane spacing?