Question 1

When a first-order spectrum is examined by means of a one-inch grating having 10,000 lines/inch,the resolving power is R.When a second-order spectrum is examined by means of a two-inch grating having 20,000 lines/inch,the resolving power is

Accepted Answer

The resolving power (R) of a grating is given by the formula R = nN, where n is the order of the spectrum and N is the total number of lines on the grating. For the first case, n = 1 and N = 10,000, so R = 1*10,000. For the second case, n = 2 and N = 2*20,000 = 40,000, so the resolving power is 2*40,000 = 80,000, which is 8 times the original R.

Question 2

Which of two diffraction gratings,one with N₁ and the other with N₂ slits per centimeter,has the greater resolving power if N₁ is greater than N₂?

Accepted Answer

The resolving power of a diffraction grating increases with the number of slits per centimeter. Therefore, the grating with more slits per centimeter (N₁) has greater resolving power.

Question 3

A parallel beam of sodium light of wavelength 589 nm is normally incident on a diffraction grating.If the second order diffraction maximum is observed at 50.25 degrees to the normal,then calculate the number of lines per cm of the grating.

Accepted Answer

The answer of A parallel beam of sodium light of...

Question 4

The yellow line of a Sodium lamp is two lines very close together at $\lambda$₁ = 589.592 nm and $\lambda$₂ = 588.995 nm.If a diffraction grating has to resolve the first order diffraction lines by an angular separation of 0.1S1U1P1$\circ$S1S1P0,what is the least number of lines per cm for the diffraction grating?

Accepted Answer

The minimum angular separation required to resolve the two lines can be calculated as:

θ = λ/d

where λ is the wavelength of light and d is the spacing between the lines on the grating.

For the first order diffraction lines, the angular separation is given as 0.1°. Therefore,

d = λ/θ

= λ/(0.1°)

= λ/(0.1 x (π/180) radians)

= λ/0.00174 radians

Now, we can calculate the spacing between the lines on the grating:

d = (589.592 nm + 588.995 nm)/2 / 0.00174 radians

= 341021 nm/rad

= 3.41021 μm/rad

Finally, we can calculate the number of lines per cm as:

N = 1/d * 10^4 lines/cm

= 1/(3.41021 μm/rad) * 10^4 lines/cm

= 2931.6 lines/cm

Rounding up to the nearest hundred gives us the answer of 2900 lines/cm, which is closest to option C (14,700 cm-1).

Question 5

If the prism spectrum of a source is a line spectrum,the grating spectrum would

Accepted Answer

Both the prism and the grating create spectra by separating the different wavelengths of light emitted by a source, but the grating creates sharper and more precise lines. So, if the prism spectrum is a line spectrum, then the grating spectrum would also be a line spectrum, but the lines would be sharper and better defined. Thus, choice D is the best answer.

Question 6

Hydrogen emits violet light with a wavelength of 410 nm and red light with a wavelength of 656 nm.A parallel beam of hydrogen light is normally incident on a diffraction grating that has 5500 lines per cm.What is the angle between the second order red line and the third order violet line that appear close together?

Accepted Answer

The angle for each order can be calculated using the diffraction grating formula: d*sin(θ) = m*λ. For the second order red line (m=2, λ=656 nm) and the third order violet line (m=3, λ=410 nm), calculate θ for each and find the difference. The correct angle difference is approximately 3.62 degrees.

Question 7

The yellow line of a Sodium lamp is two lines very close together at $\lambda$₁ = 589.592 nm and $\lambda$₂ = 588.995 nm.A diffraction grating with 10,000 lines/cm is used to resolve the lines.What is the angular separation of the two lines for the first order diffraction?

Accepted Answer

The angular separation can be found using the equation:

Δθ = λ/d

where λ is the wavelength of light, d is the spacing between the lines on the diffraction grating, and Δθ is the angular separation between the two lines.

In this case, λ = 589.592 nm - 588.995 nm = 0.597 nm (since the two lines are very close together and can be treated as one wavelength) and d = 1/10000 cm = 10⁻⁴ cm.

Plugging in these values, we get:

Δθ = (0.597 nm) / (10⁻⁴ cm) = 0.0597 radians

Converting to degrees and rounding to four significant figures, we get:

Δθ = 0.0423°

Therefore, the best choice is B with the explanation that using the equation Δθ = λ/d with the given values results in an angular separation of 0.0423 degrees between the two lines.

Question 8

White light is in one case dispersed by refraction on passing through a glass prism and in a second case diffracted by means of a grating.When the red component and the blue component are considered,it is found that

Accepted Answer

When white light passes through a glass prism, it undergoes refraction and gets split into its constituent colors due to the phenomenon of dispersion. The extent of refraction and dispersion depends on the wavelength of the light. Since Red light has the longest wavelength, it bends the least, and since blue light has the shortest wavelength, it bends the most when passing through the prism. Hence, red is refracted at a smaller angle than blue, and the answer choices A and B can be eliminated.

When white light is diffracted by a grating, interference patterns are formed, and each color is separated at specific angles, as the spacing between the gratings determines the angles at which constructive interference occurs. Again, since the separation between the gratings is inversely proportional to the wavelength of light, blue has to diffract more than red to satisfy the condition for constructive interference. Therefore, blue is diffracted at a greater angle than red. Hence, option C can be eliminated, leaving us with option D.

Therefore, the correct answer is D: blue is refracted at a greater angle than red, but red is diffracted at a greater angle than blue.

Question 9

A discharge tube is known to produce two spectral lines,one at 640 nm and the other at 640.4 nm.The total number of rulings that a grating must have to just resolve these lines in the second order is

Accepted Answer

The resolution of spectral lines using a diffraction grating is determined by the grating equation and the Rayleigh criterion for resolution. According to the Rayleigh criterion, two wavelengths, λ and λ + Δλ, are just resolved in the nth order of diffraction when their diffraction patterns are separated by the angular distance corresponding to the first minimum of one pattern coinciding with the maximum of the other. The formula for the resolving power (R) of a grating is given by R = λ/Δλ = nN, where n is the order of diffraction and N is the total number of rulings on the grating. Given: λ = 640 nm, Δλ = 0.4 nm, and n = 2 (second order).R = λ/Δλ = 640/0.4 = 1600Therefore, nN = 1600. Since n = 2, we find N by rearranging the equation to N = 1600/n = 1600/2 = 800. Thus, the grating must have at least 800 rulings to just resolve these two spectral lines in the second order.

Question 10

The spacing between the adjacent lines of a diffraction grating is the same as the distance between the two slits in the Young's double slit experiment.Both are illuminated by light of the same wavelength.In which way do the interference fringes seen on the screen differ for the two methods?

Accepted Answer

The diffraction grating produces narrower fringes due to the constructive and destructive interference from multiple slits, leading to sharper and more defined peaks compared to the broader fringes produced by the double slit experiment.

Question 11

Red light ($\lambda$ = 700 nm)is incident normally on a diffraction grating having 1000 lines/cm.A maximum is observed at a deflection angle of 12º.The order in which this occurs is

Accepted Answer

The answer of Red light ($\lambda$ = 700 nm)is incident...

Quiz 33: Interference and Diffraction

When a first-order spectrum is examined by means of a one-inch grating having 10,000 lines/inch,the resolving power is R.When a second-order spectrum is examined by means of a two-inch grating having 20,000 lines/inch,the resolving power is

Which of two diffraction gratings,one with N₁ and the other with N₂ slits per centimeter,has the greater resolving power if N₁ is greater than N₂?

A parallel beam of sodium light of wavelength 589 nm is normally incident on a diffraction grating.If the second order diffraction maximum is observed at 50.25 degrees to the normal,then calculate the number of lines per cm of the grating.

If the prism spectrum of a source is a line spectrum,the grating spectrum would

The yellow line of a Sodium lamp is two lines very close together at $\lambda$ ₁ = 589.592 nm and $\lambda$ ₂ = 588.995 nm.A diffraction grating with 10,000 lines/cm is used to resolve the lines.What is the angular separation of the two lines for the first order diffraction?

White light is in one case dispersed by refraction on passing through a glass prism and in a second case diffracted by means of a grating.When the red component and the blue component are considered,it is found that

A discharge tube is known to produce two spectral lines,one at 640 nm and the other at 640.4 nm.The total number of rulings that a grating must have to just resolve these lines in the second order is

The spacing between the adjacent lines of a diffraction grating is the same as the distance between the two slits in the Young's double slit experiment.Both are illuminated by light of the same wavelength.In which way do the interference fringes seen on the screen differ for the two methods?

Red light ( $\lambda$ = 700 nm) is incident normally on a diffraction grating having 1000 lines/cm.A maximum is observed at a deflection angle of 12º.The order in which this occurs is

Quiz 33: Interference and Diffraction

When a first-order spectrum is examined by means of a one-inch grating having 10,000 lines/inch,the resolving power is R.When a second-order spectrum is examined by means of a two-inch grating having 20,000 lines/inch,the resolving power is

Which of two diffraction gratings,one with N1 and the other with N2 slits per centimeter,has the greater resolving power if N1 is greater than N2?

A parallel beam of sodium light of wavelength 589 nm is normally incident on a diffraction grating.If the second order diffraction maximum is observed at 50.25 degrees to the normal,then calculate the number of lines per cm of the grating.

If the prism spectrum of a source is a line spectrum,the grating spectrum would

The yellow line of a Sodium lamp is two lines very close together at λ\lambdaλ 1 = 589.592 nm and λ\lambdaλ 2 = 588.995 nm.A diffraction grating with 10,000 lines/cm is used to resolve the lines.What is the angular separation of the two lines for the first order diffraction?

White light is in one case dispersed by refraction on passing through a glass prism and in a second case diffracted by means of a grating.When the red component and the blue component are considered,it is found that

A discharge tube is known to produce two spectral lines,one at 640 nm and the other at 640.4 nm.The total number of rulings that a grating must have to just resolve these lines in the second order is

The spacing between the adjacent lines of a diffraction grating is the same as the distance between the two slits in the Young's double slit experiment.Both are illuminated by light of the same wavelength.In which way do the interference fringes seen on the screen differ for the two methods?

Red light ( λ\lambdaλ = 700 nm) is incident normally on a diffraction grating having 1000 lines/cm.A maximum is observed at a deflection angle of 12º.The order in which this occurs is

Which of two diffraction gratings,one with N₁ and the other with N₂ slits per centimeter,has the greater resolving power if N₁ is greater than N₂?

The yellow line of a Sodium lamp is two lines very close together at $\lambda$ ₁ = 589.592 nm and $\lambda$ ₂ = 588.995 nm.A diffraction grating with 10,000 lines/cm is used to resolve the lines.What is the angular separation of the two lines for the first order diffraction?

Red light ( $\lambda$ = 700 nm) is incident normally on a diffraction grating having 1000 lines/cm.A maximum is observed at a deflection angle of 12º.The order in which this occurs is