Question 1

For a double slit experiment,two 1.50-mm wide slits are separated by a distance of 0.500 mm.The slits are illuminated by a laser beam with wavelength 488 nm.If the separation of the bright fringes on the screen is 5.00 mm,then how far is the screen away from the slits?

Accepted Answer

The separation of the bright fringes (Δy) on the screen can be calculated using the formula Δy = λL/d, where λ is the wavelength of the light (488 nm = 488 x 10^-9 m), L is the distance from the slits to the screen, and d is the distance between the slits (0.500 mm = 0.500 x 10^-3 m). Rearranging the formula to solve for L gives L = (Δy * d) / λ. Substituting the given values, L = (5.00 x 10^-3 m * 0.500 x 10^-3 m) / (488 x 10^-9 m) = 5.12 m.

Question 2

The element sodium emits two wavelengths of yellow light that are very close together.The wavelengths are 589.00 nm and 589.59 nm.How many narrow slits are required for a diffraction grating to be able to resolve the first-order bright fringes created by them?

Accepted Answer

D

Question 3

An airplane is made invisible to radar by coating it with a 7.0 mm thick layer of an antireflective polymer.If the maximum wavelength of radar waves for which the plane is made invisible is 4.0 cm,what is the index of refraction of the polymer?

Accepted Answer

For an antireflective coating to be effective, its optical thickness (product of physical thickness and refractive index) should be a quarter of the wavelength of the light (or in this case, radar waves) it is designed to cancel out. This means $ n \cdot d = \lambda / 4 $, where $ n $ is the refractive index, $ d $ is the thickness of the coating, and $ \lambda $ is the wavelength of the radar waves. Rearranging for $ n $, we get $ n = \lambda / (4d) $. Substituting the given values, $ n = 0.04 m / (4 \cdot 0.007 m) = 1.43 $.

Question 4

A beam of light having a wavelength of 488 nm is shone on the two slits and an interference pattern is observed.The angular separation between the central maximum and the adjacent maximum is 9.94 * 10^-4 rad.What is the distance between the two slits?

Accepted Answer

The distance between the two slits can be found using the formula:

d = λD/θ

where λ is the wavelength of the light, D is the distance between the slits and the screen, and θ is the angular separation between the central maximum and the adjacent maximum.

Substituting the given values, we get:

d = (488 nm)(1 m)/(9.94 x 10^-4 rad) = 4.91 x 10^-6 m = 4.91 x 10^-3 mm

Therefore, the best choice is (B) 4.91 x 10^-6 m.

Question 5

A Young's interference experiment is performed with monochromatic green light ($\lambda$ = 470 nm).The separation between the slits is 0.120 mm,and the interference pattern on a screen shows the first side maximum 3.5 mm from the center of the pattern.How far away from the slits is the screen?

Accepted Answer

The distance to the screen $D$ can be calculated using the formula for the position of the first side maximum in a double-slit interference pattern: $y = \frac{\lambda D}{d}$. Rearranging for $D$, we have $D = \frac{y \cdot d}{\lambda}$. Substituting $y = 3.5 \times 10^{-3}$ m, $d = 0.120 \times 10^{-3}$ m, and $\lambda = 470 \times 10^{-9}$ m, we find $D \approx 0.89$ m.

Question 6

Monochromatic light is beamed into a Michelson interferometer.600 fringes move by the screen when the movable mirror is moved a distance d = 0.125 mm.What is the wavelength of the light?

Accepted Answer

The answer of Monochromatic light is beamed into a Michelson...

Question 7

Two stars must be separated if they're to be resolved for all wavelengths of visible light.Which principle can be used to determine the minimum angular separation of the two stars in order for them to be resolved?

Accepted Answer

The correct principle for determining the minimum angular separation of two stars in order for them to be resolved is the Rayleigh criterion, which is related to the diffraction limit of a telescope or optical system. None of the options provided (Huygens' Principle, Fermat's Principle, Snell's Law of Diffraction) directly describe this criterion.

Question 8

For a double slit experiment,two 1.50 mm wide slits are separated by a distance of 0.500 mm.The slits are illuminated by a laser beam with wavelength 488 nm.If a screen is placed 10.0 m away from the slits,determine the separation of the bright fringes on the screen.

Accepted Answer

The answer of For a double slit experiment,two 1.50 mm...

Question 9

A square has sides of length L.In the lower-right and lower-left corners there are two sources of light waves,one in each corner,that emit identical in-phase light waves of wavelength 8.28 m in all directions.What is the minimum value of L such that constructive interference occurs in the upper-right corner? Ignore any reflections.

Accepted Answer

The condition for constructive interference is given by:

d sinθ = m λ

where d is the distance between the two sources (which is equal to the length of the side of the square), θ is the angle between the line connecting the sources and the line to the point of interest (in this case, the upper-right corner), m is an integer representing the order of the interference (m=1 for the first maximum), and λ is the wavelength of the light.

For the first maximum, we want to find the smallest value of L that satisfies this equation for m=1 and θ=45° (since the sources are emitting light in all directions, the angle between them and the point of interest is 45° in this case).

Substituting the values given, we get:

L (sin45°) = (1) (8.28 m)

Simplifying, we get:

L = 11.7 m

Therefore, the minimum value of L such that constructive interference occurs in the upper-right corner is 11.7 m, which is closest to choice D (20.0 m).

Question 10

Light from a laser strikes a diffraction grating that has 6500 grooves per centimeter.The interference pattern is observed on a wall 1.00 m from the grating.If the wavelength of the laser light is 454 nm,how far from the central maximum is the first order maximum?

Accepted Answer

The distance to the first order maximum can be calculated using the formula for diffraction grating: $d \sin \theta = m \lambda$. Here, $d = \frac{1}{6500 \text{ cm}^{-1}} = 1.54 \times 10^{-6} \text{ m}$, $m = 1$, and $\lambda = 454 \times 10^{-9} \text{ m}$. Solving for $\sin \theta$ gives $\sin \theta = \frac{1 \times 454 \times 10^{-9}}{1.54 \times 10^{-6}}$. The distance $x$ from the central maximum is $x = L \tan \theta \approx L \sin \theta$ for small angles, where $L = 1 \text{ m}$. Calculating gives $x \approx 0.309 \text{ nm}$.

Question 11

The distance between the slits in a double slit experiment is 5.00 *10^-4 m.A beam of light is shone on the slits.The angular separation between the central maximum and the adjacent maximum is 9.94 * 10^-4 rad.What is the wavelength of the light?

Accepted Answer

The wavelength of the light can be calculated using the formula for the angular separation in a double slit experiment, $\theta = \frac{\lambda}{d}$, where $\theta$ is the angular separation, $\lambda$ is the wavelength, and $d$ is the distance between the slits. Rearranging for $\lambda$, we get $\lambda = \theta \times d$. Substituting the given values, $\lambda = 9.94 \times 10^{-4} \, \text{rad} \times 5.00 \times 10^{-4} \, \text{m} = 497 \times 10^{-9} \, \text{m} = 497 \, \text{nm}$.

Question 12

An airplane is made invisible to radar by coating it with a layer of an antireflective polymer having an index of refraction of 1.50.What is the thickness of the polymer if the maximum wavelength of radar waves for which the plane is made invisible is 4.0 cm?

Accepted Answer

For maximum destructive interference, the thickness of the polymer layer should be a quarter of the wavelength in the medium. The wavelength in the medium ($\lambda'$) is given by $\lambda' = \lambda / n$, where $\lambda$ is the wavelength in air (4.0 cm) and $n$ is the index of refraction (1.50). Thus, $\lambda' = 4.0 \, \text{cm} / 1.5 = 2.67 \, \text{cm}$. The thickness for maximum destructive interference is $\lambda' / 4 = 2.67 \, \text{cm} / 4 = 0.667 \, \text{cm} = 6.7 \, \text{mm}$.

Question 13

Light from a laser strikes a diffraction grating that has 6500 grooves per centimeter.The central and first order principal maxima are separated by 0.325 m on a wall 1.00 m from the grating.Determine the wavelength of the laser light.

Accepted Answer

The answer of Light from a laser strikes a diffraction...

Question 14

Monochromatic blue light ($\lambda$ = 470 nm)is beamed into a Michelson interferometer.How many fringes move by the screen when the movable mirror is moved a distance d = 0.125 mm?

Accepted Answer

The answer of Monochromatic blue light ($\lambda$ = 470 nm)is...

Question 15

A square has sides of length L.In the lower-right and lower-left corners there are two sources of light waves,one in each corner,that emit identical in-phase light waves of wavelength 8.28 m in all directions.What is the minimum value of L such that destructive interference occurs in the upper-right corner? Ignore any reflections.

Accepted Answer

The answer of A square has sides of length L.In...

Question 16

The distance between the slits in a double slit experiment is 5.00 * 10^-4 m.A beam of light with a wavelength of 488 nm is shone on the slits.What is the angular separation between the central maximum and the adjacent maximum?

Accepted Answer

The formula for the angular separation between two adjacent maxima in a double slit experiment is given as θ = λ/d, where λ is the wavelength of light and d is the distance between the slits.
Substituting the given values, we get θ = (488 nm)/(5.00 x 10^-4 m) = 9.76 x 10^-4 rad = 9.76 x 10^-4 x (180/π) degrees = 0.056 degrees.
Therefore, the angular separation between the central maximum and the adjacent maximum is 9.76 x 10^-4 rad or 0.056 degrees, which is closest to option C.

Question 17

Young's double-slit experiment in 1801 showed that

Accepted Answer

Young's double-slit experiment demonstrated the wave nature of light through the observation of interference patterns, indicating that light waves can indeed interfere with each other.

Question 18

Which light wave will spread out more after passing through a narrow rectangular opening?

Accepted Answer

The phenomenon of Diffraction occurs when a wave passes through an opening (in this case, a narrow rectangular opening). The diffraction pattern that is generated by the wave depends on its wavelength. The longer the wavelength, the more the wave bends or diffracts around the edges of the opening. Therefore, a wave with a greater wavelength will spread out more after passing through the opening. Additionally, intensity does not affect diffraction. Therefore, the answer is option C as it satisfies the criteria of having a greater wavelength with a greater intensity.

Question 19

An airplane is made invisible to radar by coating it with a 7.0 mm thick layer of an antireflective polymer with the index of refraction n = 1.5.What is the maximum wavelength of radar waves for which the plane is made invisible?

Accepted Answer

The answer of An airplane is made invisible to radar...

Question 20

Monochromatic blue light ($\lambda$ = 470 nm)is beamed into a Michelson interferometer.600 fringes move by the screen when the movable mirror is moved a distance d.How far was the movable mirror moved?

Accepted Answer

The distance the movable mirror is moved, $d$, is related to the number of fringes, $N$, and the wavelength of the light, $\lambda$, by the formula $2d = N\lambda$. Given $N = 600$ and $\lambda = 470$ nm (or $470 \times 10^{-9}$ m), we can solve for $d$:$$2d = 600 \times 470 \times 10^{-9} m$$$$d = 300 \times 470 \times 10^{-9} m$$$$d = 141 \times 10^{-6} m$$$$d = 0.141 mm$$

Quiz 34: Wave Optics

For a double slit experiment,two 1.50-mm wide slits are separated by a distance of 0.500 mm.The slits are illuminated by a laser beam with wavelength 488 nm.If the separation of the bright fringes on the screen is 5.00 mm,then how far is the screen away from the slits?

The element sodium emits two wavelengths of yellow light that are very close together.The wavelengths are 589.00 nm and 589.59 nm.How many narrow slits are required for a diffraction grating to be able to resolve the first-order bright fringes created by them?

An airplane is made invisible to radar by coating it with a 7.0 mm thick layer of an antireflective polymer.If the maximum wavelength of radar waves for which the plane is made invisible is 4.0 cm,what is the index of refraction of the polymer?

A beam of light having a wavelength of 488 nm is shone on the two slits and an interference pattern is observed.The angular separation between the central maximum and the adjacent maximum is 9.94 * 10^-4 rad.What is the distance between the two slits?

A Young's interference experiment is performed with monochromatic green light ( $\lambda$ = 470 nm) .The separation between the slits is 0.120 mm,and the interference pattern on a screen shows the first side maximum 3.5 mm from the center of the pattern.How far away from the slits is the screen?

Monochromatic light is beamed into a Michelson interferometer.600 fringes move by the screen when the movable mirror is moved a distance d = 0.125 mm.What is the wavelength of the light?

Two stars must be separated if they're to be resolved for all wavelengths of visible light.Which principle can be used to determine the minimum angular separation of the two stars in order for them to be resolved?

For a double slit experiment,two 1.50 mm wide slits are separated by a distance of 0.500 mm.The slits are illuminated by a laser beam with wavelength 488 nm.If a screen is placed 10.0 m away from the slits,determine the separation of the bright fringes on the screen.

Light from a laser strikes a diffraction grating that has 6500 grooves per centimeter.The interference pattern is observed on a wall 1.00 m from the grating.If the wavelength of the laser light is 454 nm,how far from the central maximum is the first order maximum?

The distance between the slits in a double slit experiment is 5.00 10^-4 m.A beam of light is shone on the slits.The angular separation between the central maximum and the adjacent maximum is 9.94 10^-4 rad.What is the wavelength of the light?

An airplane is made invisible to radar by coating it with a layer of an antireflective polymer having an index of refraction of 1.50.What is the thickness of the polymer if the maximum wavelength of radar waves for which the plane is made invisible is 4.0 cm?

Light from a laser strikes a diffraction grating that has 6500 grooves per centimeter.The central and first order principal maxima are separated by 0.325 m on a wall 1.00 m from the grating.Determine the wavelength of the laser light.

Monochromatic blue light ( $\lambda$ = 470 nm) is beamed into a Michelson interferometer.How many fringes move by the screen when the movable mirror is moved a distance d = 0.125 mm?

The distance between the slits in a double slit experiment is 5.00 * 10^-4 m.A beam of light with a wavelength of 488 nm is shone on the slits.What is the angular separation between the central maximum and the adjacent maximum?

Young's double-slit experiment in 1801 showed that

Which light wave will spread out more after passing through a narrow rectangular opening?

An airplane is made invisible to radar by coating it with a 7.0 mm thick layer of an antireflective polymer with the index of refraction n = 1.5.What is the maximum wavelength of radar waves for which the plane is made invisible?

Monochromatic blue light ( $\lambda$ = 470 nm) is beamed into a Michelson interferometer.600 fringes move by the screen when the movable mirror is moved a distance d.How far was the movable mirror moved?

Quiz 34: Wave Optics

For a double slit experiment,two 1.50-mm wide slits are separated by a distance of 0.500 mm.The slits are illuminated by a laser beam with wavelength 488 nm.If the separation of the bright fringes on the screen is 5.00 mm,then how far is the screen away from the slits?

The element sodium emits two wavelengths of yellow light that are very close together.The wavelengths are 589.00 nm and 589.59 nm.How many narrow slits are required for a diffraction grating to be able to resolve the first-order bright fringes created by them?

An airplane is made invisible to radar by coating it with a 7.0 mm thick layer of an antireflective polymer.If the maximum wavelength of radar waves for which the plane is made invisible is 4.0 cm,what is the index of refraction of the polymer?

A beam of light having a wavelength of 488 nm is shone on the two slits and an interference pattern is observed.The angular separation between the central maximum and the adjacent maximum is 9.94 * 10-4 rad.What is the distance between the two slits?

A Young's interference experiment is performed with monochromatic green light ( λ\lambdaλ = 470 nm) .The separation between the slits is 0.120 mm,and the interference pattern on a screen shows the first side maximum 3.5 mm from the center of the pattern.How far away from the slits is the screen?

Monochromatic light is beamed into a Michelson interferometer.600 fringes move by the screen when the movable mirror is moved a distance d = 0.125 mm.What is the wavelength of the light?

Two stars must be separated if they're to be resolved for all wavelengths of visible light.Which principle can be used to determine the minimum angular separation of the two stars in order for them to be resolved?

For a double slit experiment,two 1.50 mm wide slits are separated by a distance of 0.500 mm.The slits are illuminated by a laser beam with wavelength 488 nm.If a screen is placed 10.0 m away from the slits,determine the separation of the bright fringes on the screen.

Light from a laser strikes a diffraction grating that has 6500 grooves per centimeter.The interference pattern is observed on a wall 1.00 m from the grating.If the wavelength of the laser light is 454 nm,how far from the central maximum is the first order maximum?

The distance between the slits in a double slit experiment is 5.00 *10-4 m.A beam of light is shone on the slits.The angular separation between the central maximum and the adjacent maximum is 9.94 * 10-4 rad.What is the wavelength of the light?

An airplane is made invisible to radar by coating it with a layer of an antireflective polymer having an index of refraction of 1.50.What is the thickness of the polymer if the maximum wavelength of radar waves for which the plane is made invisible is 4.0 cm?

Light from a laser strikes a diffraction grating that has 6500 grooves per centimeter.The central and first order principal maxima are separated by 0.325 m on a wall 1.00 m from the grating.Determine the wavelength of the laser light.

Monochromatic blue light ( λ\lambdaλ = 470 nm) is beamed into a Michelson interferometer.How many fringes move by the screen when the movable mirror is moved a distance d = 0.125 mm?

The distance between the slits in a double slit experiment is 5.00 * 10-4 m.A beam of light with a wavelength of 488 nm is shone on the slits.What is the angular separation between the central maximum and the adjacent maximum?

Young's double-slit experiment in 1801 showed that

Which light wave will spread out more after passing through a narrow rectangular opening?

An airplane is made invisible to radar by coating it with a 7.0 mm thick layer of an antireflective polymer with the index of refraction n = 1.5.What is the maximum wavelength of radar waves for which the plane is made invisible?

Monochromatic blue light ( λ\lambdaλ = 470 nm) is beamed into a Michelson interferometer.600 fringes move by the screen when the movable mirror is moved a distance d.How far was the movable mirror moved?

A beam of light having a wavelength of 488 nm is shone on the two slits and an interference pattern is observed.The angular separation between the central maximum and the adjacent maximum is 9.94 * 10^-4 rad.What is the distance between the two slits?

A Young's interference experiment is performed with monochromatic green light ( $\lambda$ = 470 nm) .The separation between the slits is 0.120 mm,and the interference pattern on a screen shows the first side maximum 3.5 mm from the center of the pattern.How far away from the slits is the screen?

The distance between the slits in a double slit experiment is 5.00 10^-4 m.A beam of light is shone on the slits.The angular separation between the central maximum and the adjacent maximum is 9.94 10^-4 rad.What is the wavelength of the light?

Monochromatic blue light ( $\lambda$ = 470 nm) is beamed into a Michelson interferometer.How many fringes move by the screen when the movable mirror is moved a distance d = 0.125 mm?

The distance between the slits in a double slit experiment is 5.00 * 10^-4 m.A beam of light with a wavelength of 488 nm is shone on the slits.What is the angular separation between the central maximum and the adjacent maximum?

Monochromatic blue light ( $\lambda$ = 470 nm) is beamed into a Michelson interferometer.600 fringes move by the screen when the movable mirror is moved a distance d.How far was the movable mirror moved?