Question 1

A diffraction grating has 5000 lines per centimeter and is 1.5 centimeters wide.When radiation is incident upon the grating a second-order maximum is observed at an angle of 37º.The wavelength of this light is

Accepted Answer

The wavelength ($\lambda$) can be found using the 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 5000 lines per cm, the spacing $d = \frac{1}{5000 \text{ lines/cm}} = \frac{1}{500000 \text{ lines/m}} = 2 \times 10^{-6} \text{ m}$. For the second-order maximum ($m = 2$) at $37^\circ$, solving for $\lambda$ gives $\lambda = \frac{d\sin(\theta)}{m} = \frac{2 \times 10^{-6} \text{ m} \times \sin(37^\circ)}{2} \approx 600 \text{ nm}$.

Question 2

For a given light source and collimator slit width,the spectral lines obtained using a prism are brighter than those using a diffraction grating because

Accepted Answer

A prism disperses light by refracting it through a prism of a certain material that bends the light at different angles based on its wavelength. On the other hand, a diffraction grating disperses light by diffracting it through a series of closely spaced, parallel lines that create interference when the light passes through it. The interference causes the light to split into its various wavelengths. The prism disperses light more than a grating, which causes the spectral lines to appear brighter.

Question 3

In accordance with the Rayleigh criterion,two points can be just resolved if the centers of their diffraction patterns are separated by

Accepted Answer

According to the Rayleigh criterion, two points are just resolved when the center of one diffraction pattern falls on the first minimum of the other. This corresponds to a separation of one-half the width of the central maximum.

Question 4

The type of electromagnetic radiation that is employed when crystals are used as diffraction gratings is

Accepted Answer

Crystals are often used as diffraction gratings for X-ray crystallography, which uses X-rays to determine the three-dimensional structures of molecules. X-rays have short wavelengths (on the order of angstroms) that allow them to interact with the regular arrangement of atoms in a crystal lattice, producing a diffraction pattern that can be analyzed to determine the structure of the molecule. Other forms of electromagnetic radiation, such as visible light or microwaves, would not have wavelengths small enough to interact with the crystal lattice in the same way as X-rays.

Question 5

Rayleigh's criterion is most closely associated with

Accepted Answer

Rayleigh's criterion is most closely associated with diffraction, which describes the spreading out of waves as they pass through an aperture or obstacle. The criterion sets a limit for how close two objects can be before they are no longer distinguished as separate by an optical instrument.

Question 6

A diffraction grating has 2000 lines per centimeter and is 3.0 centimeters wide.When visible light is incident on the grating,a maximum is observed at an angle of 10º from the normal.The wavelength of the incident radiation is

Accepted Answer

The formula for finding the wavelength of the incident radiation for a diffraction grating is:

λ = d sinθ / N

where λ is the wavelength of light, d is the distance between adjacent lines on the grating, θ is the angle from the normal at which the maximum is observed, and N is the number of lines per unit length.

Plugging in the values, we get:

λ = (3.0 cm / 2000 lines/cm) sin(10º) 
   = 5.25 x 10^-5 cm 
   = 525 nm

Therefore, the wavelength of the incident radiation is 525 nm, which corresponds to choice B.

Question 7

You illuminate a slit 0.20 mm wide with monochromatic light of wavelength 590 nm,and focus the Fraunhofer diffraction pattern on a screen with a lens of focal length 2.00 m.The distance between the two dark fringes on each side of the central bright fringe is

Accepted Answer

The distance between the two dark fringes on each side of the central bright fringe is given by:

d = (λL)/w

where λ is the wavelength of light, L is the distance between the slit and the screen (in this case L = 2.00 m), and w is the width of the slit (w = 0.20 mm = 2.0 × 10^−4 m).

Substituting the given values, we get:

d = (590 × 10^−9 m) × (2.00 m) / (2.0 × 10^−4 m) = 5.90 × 10^−3 m = 1.18 cm.

Therefore, the correct choice is C.

Question 8

Green light of wavelength 500 nm is incident normally on a diffraction grating that has 5300 lines/cm.The second-order image is diffracted at an angle from the normal of

Accepted Answer

The equation for diffraction on a grating is: 
d sinθ = mλ
where 
d = distance between adjacent slits
θ = angle of diffraction
m = order of diffraction
λ = wavelength of light

Using the given values:
d = 1 / (5300 lines/cm) = 1.8868 x 10^-4 cm
m = 2
λ = 500 nm = 5 x 10^-5 cm

Substituting into the equation, we get:
d sinθ = mλ
1.8868 x 10^-4 cm x sinθ = 2 x 5 x 10^-5 cm
sinθ = 0.53
θ = sin^-1(0.53) = 32º

Therefore, the answer is C) 32º.

Question 9

For a given grating,it is observed that a third-order line (m = 3)with $\lambda$ = 465.3 nm overlaps a second-order line (has the same $\theta$ as a line with m = 2).The wavelength of the second-order line is

Accepted Answer

Let's use the grating equation:

mλ = d(sinθ + sinϕ)

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

For the third-order line:

3(465.3 nm) = d(sinθ + sinϕ1)

For the second-order line:

2λ = d(sinθ + sinϕ2)

We know that both lines have the same F1F1F1S1θF1F1F10 (angle of incidence), so we can equate the values:

sinθ + sinϕ1 = sinθ + sinϕ2

sinϕ1 = sinϕ2

Now we can substitute sinϕ1 for sinϕ2 in the second equation:

2λ = d(sinθ + sinϕ1)

2λ = 3(465.3 nm)

λ = 697.95 nm

The closest answer choice is B, 698 nm.

Question 10

The size of the smallest things that can be seen with an optical microscope is limited by diffraction.Which of the following could help a microscopist see smaller things?

Accepted Answer

The size of the smallest things that can be seen with an optical microscope is limited by diffraction. The diffraction limit can be improved by using light with a shorter wavelength, which allows for better resolution. Therefore, using light with a shorter wavelength could help a microscopist see smaller things.

Question 11

The headlights of an oncoming car are 1.2 m apart.What is the maximum distance from the car at which you can resolve the lights as two sources if the diameter of the pupil of your eye is 5.0 mm and the wavelength of the light is 555 nm?

Accepted Answer

The resolution of two sources as distinct depends on the Rayleigh criterion, which is given by the formula $\theta = 1.22 \frac{\lambda}{D}$, where $\theta$ is the angular resolution in radians, $\lambda$ is the wavelength of light, and $D$ is the diameter of the aperture (in this case, the pupil of the eye). To find the maximum distance ($L$) at which the car's headlights can be resolved, we use the formula $\theta = \frac{s}{L}$, where $s$ is the separation between the headlights. Combining the two gives $L = \frac{sD}{1.22\lambda}$.Given: $s = 1.2$ m, $D = 5.0$ mm = $0.005$ m, and $\lambda = 555$ nm = $555 \times 10^{-9}$ m.Substituting these values gives:$$L = \frac{1.2 \times 0.005}{1.22 \times 555 \times 10^{-9}} \approx 8900 \, \text{m} = 8.9 \, \text{km}.$$

Question 12

The pupil of the human eye has a diameter of about 5 mm.When the wavelength of light incident on the pupil is 500 nm,the smallest angular separation of two resolvable sources is approximately

Accepted Answer

The answer of The pupil of the human eye has...

Question 13

You illuminate a slit 0.20 mm wide with monochromatic light of wavelength 600 nm,and focus the Fraunhofer diffraction pattern on a screen with a lens of focal length 1.50 m.The distance on the screen from the center of the central maximum to the first minimum is

Accepted Answer

The answer of You illuminate a slit 0.20 mm wide...

Question 14

For a grating with d = 3.5$\lambda$,the maximum order m of an interference maximum that can be observed for a specified $\lambda$ is

Accepted Answer

The maximum order m is given by the formula m = d/λ, where d is the grating spacing and λ is the wavelength. Since d = 3.5λ, the maximum integer value for m is 3.

Question 15

Diffraction occurs when light passes

Accepted Answer

Diffraction is a phenomenon that occurs when a wave encounters an obstacle or a slit that is comparable in size to its wavelength. It can happen with any type of wave, including light. When light passes by a small particle, through a small hole, through a double slit, or by a sharp edge, it can spread out instead of traveling in straight lines. This spreading out of light waves around obstacles or through openings is what we observe as diffraction. Therefore, diffraction can occur in all the conditions listed.

Question 16

A monochromatic beam of light of wavelength 600 nm falls on a grating at normal incidence and produces a second-order image at an angle of 30º.The grating spacing must be

Accepted Answer

The grating equation is d*sin(θ) = m*λ, where d is the grating spacing, θ is the angle, m is the order, and λ is the wavelength. For m=2, λ=600 nm, and θ=30º, solving gives d = 2.4 µm.

Question 17

In demonstrating single-slit Fraunhofer diffraction,decreasing the wavelength of the light while keeping the slit width constant

Accepted Answer

According to the equation for single-slit Fraunhofer diffraction, the width of the central maximum is proportional to the wavelength of the light and inversely proportional to the width of the slit. When the wavelength is decreased while keeping the slit width constant, the width of the central maximum decreases. Therefore, the correct choice is E.

Question 18

The 200-in reflecting telescope at Mt.Palomar has an objective mirror with a focal length of 16.8 m.The effective aperture is the diameter of the 200-in mirror (200 in = 5.08 m).For light in the blue region (450 nm),what is the smallest angle between two stars that this telescope can ideally resolve? (In practice,the limit of resolution is due to atmospheric turbulence.)

Accepted Answer

The smallest angle that can be resolved by a telescope is given by the Rayleigh criterion:

θ = 1.22 λ/D

where θ is the smallest angle that can be resolved, λ is the wavelength of light, and D is the diameter of the objective mirror (i.e. the effective aperture).

Substituting the values given in the problem statement, we get:

θ = 1.22 (450 nm)/(5.08 m) = 1.1 x 10^-7 radians

Therefore, the answer is B, which is the closest to this value in scientific notation.

Question 19

For a grating with d = 4.5$\lambda$,the maximum order m of an interference maximum that can be observed for a specified $\lambda$ is

Accepted Answer

The answer of For a grating with d = 4.5$\lambda$,the...

Question 20

An antenna for receiving television signals from a satellite has a diameter of 3 m.The signals have a wavelength of 24 cm.If the diameter of the antenna is reduced to 50 cm,for what signal wavelengths does the antenna still have the same angular resolution?

Accepted Answer

For an antenna to have the same angular resolution, the ratio of its diameter (D) to the wavelength (λ) should be constant. This is commonly referred to as the Rayleigh criterion. 
So, we can write:
D1/λ1 = D2/λ2
Where D1 = 3 m, λ1 = 24 cm = 0.24 m, and D2 = 0.5 m (reduced diameter).
We can solve for the wavelength that satisfies the above equation:
λ2 = (D2/D1)λ1 = (0.5/3) x 0.24 = 0.04 m = 4.0 cm
Therefore, the antenna will have the same angular resolution for signals with a wavelength of 4.0 cm. 
The other wavelengths given in the answer choices are either too small or too large, and therefore, the antenna will not have the same angular resolution for those wavelengths.

Quiz 33: Interference and Diffraction

A diffraction grating has 5000 lines per centimeter and is 1.5 centimeters wide.When radiation is incident upon the grating a second-order maximum is observed at an angle of 37º.The wavelength of this light is

For a given light source and collimator slit width,the spectral lines obtained using a prism are brighter than those using a diffraction grating because

In accordance with the Rayleigh criterion,two points can be just resolved if the centers of their diffraction patterns are separated by

The type of electromagnetic radiation that is employed when crystals are used as diffraction gratings is

Rayleigh's criterion is most closely associated with

A diffraction grating has 2000 lines per centimeter and is 3.0 centimeters wide.When visible light is incident on the grating,a maximum is observed at an angle of 10º from the normal.The wavelength of the incident radiation is

You illuminate a slit 0.20 mm wide with monochromatic light of wavelength 590 nm,and focus the Fraunhofer diffraction pattern on a screen with a lens of focal length 2.00 m.The distance between the two dark fringes on each side of the central bright fringe is

Green light of wavelength 500 nm is incident normally on a diffraction grating that has 5300 lines/cm.The second-order image is diffracted at an angle from the normal of

For a given grating,it is observed that a third-order line (m = 3) with $\lambda$ = 465.3 nm overlaps a second-order line (has the same $\theta$ as a line with m = 2) .The wavelength of the second-order line is

The size of the smallest things that can be seen with an optical microscope is limited by diffraction.Which of the following could help a microscopist see smaller things?

The headlights of an oncoming car are 1.2 m apart.What is the maximum distance from the car at which you can resolve the lights as two sources if the diameter of the pupil of your eye is 5.0 mm and the wavelength of the light is 555 nm?

The pupil of the human eye has a diameter of about 5 mm.When the wavelength of light incident on the pupil is 500 nm,the smallest angular separation of two resolvable sources is approximately

You illuminate a slit 0.20 mm wide with monochromatic light of wavelength 600 nm,and focus the Fraunhofer diffraction pattern on a screen with a lens of focal length 1.50 m.The distance on the screen from the center of the central maximum to the first minimum is

For a grating with d = 3.5 $\lambda$ ,the maximum order m of an interference maximum that can be observed for a specified $\lambda$ is

Diffraction occurs when light passes

A monochromatic beam of light of wavelength 600 nm falls on a grating at normal incidence and produces a second-order image at an angle of 30º.The grating spacing must be

In demonstrating single-slit Fraunhofer diffraction,decreasing the wavelength of the light while keeping the slit width constant

For a grating with d = 4.5 $\lambda$ ,the maximum order m of an interference maximum that can be observed for a specified $\lambda$ is

An antenna for receiving television signals from a satellite has a diameter of 3 m.The signals have a wavelength of 24 cm.If the diameter of the antenna is reduced to 50 cm,for what signal wavelengths does the antenna still have the same angular resolution?

Quiz 33: Interference and Diffraction

A diffraction grating has 5000 lines per centimeter and is 1.5 centimeters wide.When radiation is incident upon the grating a second-order maximum is observed at an angle of 37º.The wavelength of this light is

For a given light source and collimator slit width,the spectral lines obtained using a prism are brighter than those using a diffraction grating because

In accordance with the Rayleigh criterion,two points can be just resolved if the centers of their diffraction patterns are separated by

The type of electromagnetic radiation that is employed when crystals are used as diffraction gratings is

Rayleigh's criterion is most closely associated with

A diffraction grating has 2000 lines per centimeter and is 3.0 centimeters wide.When visible light is incident on the grating,a maximum is observed at an angle of 10º from the normal.The wavelength of the incident radiation is

You illuminate a slit 0.20 mm wide with monochromatic light of wavelength 590 nm,and focus the Fraunhofer diffraction pattern on a screen with a lens of focal length 2.00 m.The distance between the two dark fringes on each side of the central bright fringe is

Green light of wavelength 500 nm is incident normally on a diffraction grating that has 5300 lines/cm.The second-order image is diffracted at an angle from the normal of

For a given grating,it is observed that a third-order line (m = 3) with λ\lambdaλ = 465.3 nm overlaps a second-order line (has the same θ\thetaθ as a line with m = 2) .The wavelength of the second-order line is

The size of the smallest things that can be seen with an optical microscope is limited by diffraction.Which of the following could help a microscopist see smaller things?

The headlights of an oncoming car are 1.2 m apart.What is the maximum distance from the car at which you can resolve the lights as two sources if the diameter of the pupil of your eye is 5.0 mm and the wavelength of the light is 555 nm?

The pupil of the human eye has a diameter of about 5 mm.When the wavelength of light incident on the pupil is 500 nm,the smallest angular separation of two resolvable sources is approximately

You illuminate a slit 0.20 mm wide with monochromatic light of wavelength 600 nm,and focus the Fraunhofer diffraction pattern on a screen with a lens of focal length 1.50 m.The distance on the screen from the center of the central maximum to the first minimum is

For a grating with d = 3.5 λ\lambdaλ ,the maximum order m of an interference maximum that can be observed for a specified λ\lambdaλ is

Diffraction occurs when light passes

A monochromatic beam of light of wavelength 600 nm falls on a grating at normal incidence and produces a second-order image at an angle of 30º.The grating spacing must be

In demonstrating single-slit Fraunhofer diffraction,decreasing the wavelength of the light while keeping the slit width constant

For a grating with d = 4.5 λ\lambdaλ ,the maximum order m of an interference maximum that can be observed for a specified λ\lambdaλ is

An antenna for receiving television signals from a satellite has a diameter of 3 m.The signals have a wavelength of 24 cm.If the diameter of the antenna is reduced to 50 cm,for what signal wavelengths does the antenna still have the same angular resolution?

For a given grating,it is observed that a third-order line (m = 3) with $\lambda$ = 465.3 nm overlaps a second-order line (has the same $\theta$ as a line with m = 2) .The wavelength of the second-order line is

For a grating with d = 3.5 $\lambda$ ,the maximum order m of an interference maximum that can be observed for a specified $\lambda$ is

For a grating with d = 4.5 $\lambda$ ,the maximum order m of an interference maximum that can be observed for a specified $\lambda$ is