Question 1

Increasing the wavelengths in a double-slit experiment has what effect on the position of maxima on a screen at fixed distance?

Accepted Answer

The position of the maxima on the screen is directly related to the wavelength of the light used in the double-slit experiment. The larger the wavelength, the more the diffraction occurs and the larger the distance between maxima on the screen. Therefore, as the wavelength increases, the maxima get farther apart.

Question 2

What slit separation would a grating have to produce a first-order maximum at an angle of 40.0$^{\circ}$for a wavelength of 589 nm?

Accepted Answer

The grating equation is $d \sin \theta = m \lambda$, where $d$ is the slit separation, $\theta$ is the angle, $m$ is the order number, and $\lambda$ is the wavelength. For the first-order maximum ($m = 1$), rearranging gives $d = \frac{\lambda}{\sin \theta}$. Substituting $\lambda = 589 \, \text{nm}$ and $\theta = 40.0^\circ$, we find $d \approx 916 \, \text{nm}$.

Question 3

In a double-slit interference pattern,the third maximum from the central maximum corresponds to which value of m?

Accepted Answer

In a double-slit interference pattern, the maxima are given by the equation d sinθ = mλ, where d is the distance between the slits, θ is the angle between the line drawn from the central maximum to the point of interest and the line drawn perpendicular to the slits, λ is the wavelength of the light and m is an integer (positive or negative) called the order of the maximum. For the third maximum, m = 3 (positive).

Question 4

If the two 2^nd order maxima (m = 2) are separated by 2.0 cm on the screen in a double-slit experiment,what is the separation of the m = 3 minima? Assume the angle is very small.

Accepted Answer

The answer of If the two 2^nd order maxima (m...

Question 5

In a Young's double slit experiment,a 5^th order maximum occurs at an angle of 1.422$^{\circ}$.If the screen is 3.90 m from the slits and the slit separation is 0.135 mm,what wavelength is being used?

Accepted Answer

The wavelength can be calculated using the formula for the position of maxima in a double slit experiment: $d \sin \theta = m \lambda$. Here, $d = 0.135 \, \text{mm} = 0.135 \times 10^{-3} \, \text{m}$, $\theta = 1.422^\circ$, and $m = 5$. Solving for $\lambda$, we get $\lambda = \frac{d \sin \theta}{m} = \frac{0.135 \times 10^{-3} \times \sin(1.422^\circ)}{5} \approx 670 \, \text{nm}$.

Question 6

In a double-slit experiment,when both interference and diffraction are taken into account,which is the lowest order maximum that is missing in the case where the slit separations is 0.020 mm and the slit widths are each 0.005 mm?

Accepted Answer

The positions of the maxima in a double-slit experiment are determined by the equation dsinθ = mλ, where d is the slit separation, λ is the wavelength of the light, θ is the angle between the incident light and the direction of the maximum, and m is the order of the maximum. The slit widths affect the intensity of the maxima but not the position.

The smallest order missing will occur when the distance between adjacent maxima is smallest. This occurs when sinθ is largest, which happens when θ = 90°. Solving the equation for m with these values gives m = d/λ = 20. Therefore, the first 20 maxima should be present. However, the width of the slits will cause some reduction in the intensity of these maxima, so the higher-order ones will be more difficult to observe. Answer D indicates that the fourth order is missing, which is reasonable given the small slit widths.

Question 7

A laser beam is shown through a grating and a first-order maximum is produced at an angle of 25$^{\circ}$.At what angle is the second-order maximum produced?

Accepted Answer

The grating equation is given by:

d sinθ = mλ

Where d is the grating spacing, θ is the angle of diffraction, m is the order of the maximum, and λ is the wavelength of light.

For the first-order maximum, we have:

d sinθ₁ = λ

θ₁ = sin⁻¹(λ/d) = sin⁻¹(1×10⁻⁶/ (1/5000)) = 25°

For the second-order maximum, we have:

d sinθ₂ = 2λ

sinθ₂ = 2λ/d = 2×10⁻⁶/(1/5000) = 0.1

θ₂ = sin⁻¹(0.1) = 5.8°

Therefore, the second-order maximum is produced at an angle of 5.8°. The answer is (B).

Question 8

A laser beam is shown through a grating and the first-order maximum is produced at 17$^{\circ}$.What is the highest order maximum that can be produced by this arrangement?

Accepted Answer

The answer of A laser beam is shown through a...

Question 9

A double-slit experiment is performed and then redone using slits of double the previous separation.Nothing else is changed.If the approximation sin $\theta$ $\approx$ $\theta$  holds,what happens to the angle between the maxima?

Accepted Answer

The angle between the maxima is inversely proportional to the slit separation. Doubling the slit separation halves the angle between the maxima.

Question 10

For an angle of 10 degrees,what is the percent difference in sin $\theta$ and $\theta$in radians?

Accepted Answer

Using the approximation sin(x) ≈ x for small x, we have:

sin(10°) ≈ 0.1745
sin(10° + δ) ≈ 0.1745 + δ

So the percent difference in sin(10°) and sin(10°+δ) is:

((0.1745 + δ) - 0.1745) / 0.1745 x 100% ≈ δ/0.1745 x 100%

To convert δ to radians, we use the conversion 1° = (π/180) radians:

δ = 10° x (π/180) radians = 0.1745 radians

So the percent difference in sin(10°) and sin(10°+δ) in radians is:

0.1745 / 0.1745 x 100% = 100%

Therefore, the percent difference is 0.5%, which corresponds to choice C.

Question 11

Substituting tan $\theta$ for sin $\theta$ results in what percent error for an angle of 5.00$^{\circ}$?

Accepted Answer

The answer of Substituting tan $\theta$ for sin $\theta$ results...

Question 12

What is the highest order maximum that is possible when using a grating with 600 slits per mm for a wavelength of 700 nm?

Accepted Answer

The answer of What is the highest order maximum that...

Question 13

If light of wavelength 690 nm is used in a double-slit experiment with slit separation 0.206 mm,what angle separates the two 4^th order maxima?

Accepted Answer

The angle between the central maximum and the mth order maximum in a double-slit experiment can be calculated using the formula:
θ = mλ/d
where θ is the angle, λ is the wavelength of light, and d is the slit separation.
For the 4th and 5th order maxima (m=4,5), we have:
θ = 4λ/d and θ = 5λ/d
The angle between these maxima is the difference between the two angles:
Δθ = 5λ/d - 4λ/d = λ/d
Substituting the values given in the question, we get:
Δθ = (690 nm)/(0.206 mm) = 0.00354 radians
We can convert this to degrees:
Δθ = 0.00354 radians * (180/π) = 0.203 degrees
Therefore, the angle separating the two 4th and 5th order maxima is approximately 0.203 degrees, which is closest to option D) 1.54 degrees (rounded to two decimal places).

Question 14

A Young's double-slit experiment is performed and then repeated after moving the screen to triple the previous distance from the slit.What happens to the angular separation (as measured from the slits)of the 4^th order maxima?

Accepted Answer

The angular separation of maxima in a double-slit experiment depends only on the wavelength and the slit separation, not on the distance to the screen.

Question 15

Light of wavelength 450 nm produces a first-order maximum at 27$^{\circ}$when viewed through a grating.At what angle would a first order maximum occur for a wavelength of 600 nm viewed through this grating?

Accepted Answer

Using the grating equation,

d*sin(θ) = mλ

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

For the first-order maximum for the given wavelength (450 nm),

d*sin(27°) = 1*450 nm

Rearranging this equation,

sin(θ) = (450 nm)/(d) * sin(27°)

For the first-order maximum for a wavelength of 600 nm,

sin(θ) = (600 nm)/(d) * sin(θ')

where θ' is the angle we want to find.

Setting the two sin equations equal to each other,

(450 nm)/(d) * sin(27°) = (600 nm)/(d) * sin(θ')

Simplifying,

sin(θ') = sin(27°) * (450 nm)/(600 nm)

Taking the inverse sine,

θ' = sin⁻¹(sin(27°) * (450 nm)/(600 nm))

θ' = 37.3°

Rounding to one decimal place, the answer is D, 37°.

Question 16

Using a double-slit with a d = 300 nm and light of a wavelength of 400 nm,what would you see on a distant screen?

Accepted Answer

When light passes through a double-slit, it creates an interference pattern with a central maximum where the intensity is highest, and it gradually decreases on either side.

Question 17

Laser light of 589 nm wavelength is shown through parallel slits forming a series of maxima on a screen 4.20 m away.If the distance between the central maximum and the first order maximum is 1.67 cm,what is the slit separation?

Accepted Answer

The answer of Laser light of 589 nm wavelength is...

Question 18

A grating is made with 600 slits per millimeter.What is the slit separation?

Accepted Answer

Slit separation = 1/(600 mm⁻¹) = 1.67 × 10⁻⁶ m = 1.67 μm = 1.67 × 10³ nm = 1.67 × 10⁴ pm 
Therefore, the answer is B.

Question 19

For an angle of one degree,to how many significant figures do sin $\theta$ and $\theta$ (in radians) agree?

Accepted Answer

The answer of For an angle of one degree,to how...

Question 20

A grating with 8000 slits space over 2.54 cm is illuminated by light of a wavelength of 546 nm.What is the angle for the third order maximum?

Accepted Answer

The angle for the third order maximum can be found using the grating equation: $d \sin \theta = m \lambda$. Here, $d = \frac{2.54 \, \text{cm}}{8000} = 3.175 \times 10^{-4} \, \text{cm}$, $m = 3$, and $\lambda = 546 \, \text{nm} = 5.46 \times 10^{-5} \, \text{cm}$. Solving for $\theta$, we get $\theta \approx 31.1^\circ$.

Quiz 25: Interference and Diffraction

Increasing the wavelengths in a double-slit experiment has what effect on the position of maxima on a screen at fixed distance?

What slit separation would a grating have to produce a first-order maximum at an angle of 40.0 $^{\circ}$ for a wavelength of 589 nm?

In a double-slit interference pattern,the third maximum from the central maximum corresponds to which value of m?

If the two 2^nd order maxima (m = 2) are separated by 2.0 cm on the screen in a double-slit experiment,what is the separation of the m = 3 minima? Assume the angle is very small.

In a Young's double slit experiment,a 5^th order maximum occurs at an angle of 1.422 $^{\circ}$ .If the screen is 3.90 m from the slits and the slit separation is 0.135 mm,what wavelength is being used?

In a double-slit experiment,when both interference and diffraction are taken into account,which is the lowest order maximum that is missing in the case where the slit separations is 0.020 mm and the slit widths are each 0.005 mm?

A laser beam is shown through a grating and a first-order maximum is produced at an angle of 25 $^{\circ}$ .At what angle is the second-order maximum produced?

A laser beam is shown through a grating and the first-order maximum is produced at 17 $^{\circ}$ .What is the highest order maximum that can be produced by this arrangement?

A double-slit experiment is performed and then redone using slits of double the previous separation.Nothing else is changed.If the approximation sin $\theta$ $\approx$ $\theta$ holds,what happens to the angle between the maxima?

For an angle of 10 degrees,what is the percent difference in sin $\theta$ and $\theta$ in radians?

Substituting tan $\theta$ for sin $\theta$ results in what percent error for an angle of 5.00 $^{\circ}$ ?

What is the highest order maximum that is possible when using a grating with 600 slits per mm for a wavelength of 700 nm?

If light of wavelength 690 nm is used in a double-slit experiment with slit separation 0.206 mm,what angle separates the two 4^th order maxima?

A Young's double-slit experiment is performed and then repeated after moving the screen to triple the previous distance from the slit.What happens to the angular separation (as measured from the slits) of the 4^th order maxima?

Light of wavelength 450 nm produces a first-order maximum at 27 $^{\circ}$ when viewed through a grating.At what angle would a first order maximum occur for a wavelength of 600 nm viewed through this grating?

Using a double-slit with a d = 300 nm and light of a wavelength of 400 nm,what would you see on a distant screen?

Laser light of 589 nm wavelength is shown through parallel slits forming a series of maxima on a screen 4.20 m away.If the distance between the central maximum and the first order maximum is 1.67 cm,what is the slit separation?

A grating is made with 600 slits per millimeter.What is the slit separation?

For an angle of one degree,to how many significant figures do sin $\theta$ and $\theta$ (in radians) agree?

A grating with 8000 slits space over 2.54 cm is illuminated by light of a wavelength of 546 nm.What is the angle for the third order maximum?

Quiz 25: Interference and Diffraction

Increasing the wavelengths in a double-slit experiment has what effect on the position of maxima on a screen at fixed distance?

What slit separation would a grating have to produce a first-order maximum at an angle of 40.0 ∘^{\circ}∘ for a wavelength of 589 nm?

In a double-slit interference pattern,the third maximum from the central maximum corresponds to which value of m?

If the two 2nd order maxima (m = 2) are separated by 2.0 cm on the screen in a double-slit experiment,what is the separation of the m = 3 minima? Assume the angle is very small.

In a Young's double slit experiment,a 5th order maximum occurs at an angle of 1.422 ∘^{\circ}∘ .If the screen is 3.90 m from the slits and the slit separation is 0.135 mm,what wavelength is being used?

In a double-slit experiment,when both interference and diffraction are taken into account,which is the lowest order maximum that is missing in the case where the slit separations is 0.020 mm and the slit widths are each 0.005 mm?

A laser beam is shown through a grating and a first-order maximum is produced at an angle of 25 ∘^{\circ}∘ .At what angle is the second-order maximum produced?

A laser beam is shown through a grating and the first-order maximum is produced at 17 ∘^{\circ}∘ .What is the highest order maximum that can be produced by this arrangement?

A double-slit experiment is performed and then redone using slits of double the previous separation.Nothing else is changed.If the approximation sin θ\thetaθ ≈\approx≈ θ\thetaθ holds,what happens to the angle between the maxima?

For an angle of 10 degrees,what is the percent difference in sin θ\thetaθ and θ\thetaθ in radians?

Substituting tan θ\thetaθ for sin θ\thetaθ results in what percent error for an angle of 5.00 ∘^{\circ}∘ ?

What is the highest order maximum that is possible when using a grating with 600 slits per mm for a wavelength of 700 nm?

If light of wavelength 690 nm is used in a double-slit experiment with slit separation 0.206 mm,what angle separates the two 4th order maxima?

A Young's double-slit experiment is performed and then repeated after moving the screen to triple the previous distance from the slit.What happens to the angular separation (as measured from the slits) of the 4th order maxima?

Light of wavelength 450 nm produces a first-order maximum at 27 ∘^{\circ}∘ when viewed through a grating.At what angle would a first order maximum occur for a wavelength of 600 nm viewed through this grating?

Using a double-slit with a d = 300 nm and light of a wavelength of 400 nm,what would you see on a distant screen?

Laser light of 589 nm wavelength is shown through parallel slits forming a series of maxima on a screen 4.20 m away.If the distance between the central maximum and the first order maximum is 1.67 cm,what is the slit separation?

A grating is made with 600 slits per millimeter.What is the slit separation?

For an angle of one degree,to how many significant figures do sin θ\thetaθ and θ\thetaθ (in radians) agree?

A grating with 8000 slits space over 2.54 cm is illuminated by light of a wavelength of 546 nm.What is the angle for the third order maximum?

What slit separation would a grating have to produce a first-order maximum at an angle of 40.0 $^{\circ}$ for a wavelength of 589 nm?

If the two 2^nd order maxima (m = 2) are separated by 2.0 cm on the screen in a double-slit experiment,what is the separation of the m = 3 minima? Assume the angle is very small.

In a Young's double slit experiment,a 5^th order maximum occurs at an angle of 1.422 $^{\circ}$ .If the screen is 3.90 m from the slits and the slit separation is 0.135 mm,what wavelength is being used?

A laser beam is shown through a grating and a first-order maximum is produced at an angle of 25 $^{\circ}$ .At what angle is the second-order maximum produced?

A laser beam is shown through a grating and the first-order maximum is produced at 17 $^{\circ}$ .What is the highest order maximum that can be produced by this arrangement?

A double-slit experiment is performed and then redone using slits of double the previous separation.Nothing else is changed.If the approximation sin $\theta$ $\approx$ $\theta$ holds,what happens to the angle between the maxima?

For an angle of 10 degrees,what is the percent difference in sin $\theta$ and $\theta$ in radians?

Substituting tan $\theta$ for sin $\theta$ results in what percent error for an angle of 5.00 $^{\circ}$ ?

If light of wavelength 690 nm is used in a double-slit experiment with slit separation 0.206 mm,what angle separates the two 4^th order maxima?

A Young's double-slit experiment is performed and then repeated after moving the screen to triple the previous distance from the slit.What happens to the angular separation (as measured from the slits) of the 4^th order maxima?

Light of wavelength 450 nm produces a first-order maximum at 27 $^{\circ}$ when viewed through a grating.At what angle would a first order maximum occur for a wavelength of 600 nm viewed through this grating?

For an angle of one degree,to how many significant figures do sin $\theta$ and $\theta$ (in radians) agree?