Multi-choice questions
- Page ID
- 105491
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Multi-choice Quiz Module 3
1. Given a Gaussian beam with a wavelength of 500 nm and a beam waist of 2 mm. What is its Rayleigh range?
a. Approximately 50 meters
b. Approximately 25 meters
c. Approximately 12 meters
2. What is the radius of curvature R(z) given a q parameter q = 5 + j2?
a. 14.5 m
b. 2.32 m
c. 5.8 m
d. 36.25 m
3. What is the beam waist of a He-Ne laser (wavelength 633 nm) if its beam divergence is 2 deg?
a. The beam waist is 0.17 μm
b. There is a need to know another parameter of the Gaussian beam in order to compute the beam waist.
c. The beam waist is 5.77 μm.
4. Which one of the following sentences is not correct?
a. The larger the beam waist, the larger the depth of focus.
b. The shorter the wavelength, the larger the depth of focus
c. The depth of focus depends proportionally on the beam waist, but it is invariant with the source’s wavelength.
5. Which one of the following sentences is false?
a. The beam width always increases with the axial distance z.
b. The power of a Gaussian beam is independent of the axial distance z.
c. The power of a Gaussian beam follows a Gaussian function.
6. Consider a green laser of wavelength λ = 532 nm that emits a Gaussian beam with a beam waist of 160 μm. At a particular axial plane, the beam waist has been increased to 1 mm. What is the distance of this plane with respect to the beam waist?
a. The axial distance z is 93.26 cm.
b. The axial distance is 6.17 m.
c. There is a need for some extra parameters to solve this problem.
7. A Gaussian beam, which is propagated through the positive z-axis, is reflected by a planar mirror located perpendicular to its axis. Which of the following sentences is true?
a. The position of the beam waist depends on the radius of curvature of the planar mirror.
b. Both the beam waist and the Rayleigh distance remain the same.
c. The beam waist after the reflection is double the incident beam waist due to the reflection phenomenon.
8. A Gaussian beam, which is propagated through the positive z-axis, is transmitted by a distance d through free space. Which of the following sentences is false?
a. The axial distance d changes the value of the beam waist inversely.
b. Both the beam waist and the Raleigh distance remain invariant to this free-propagation distance.
c. The free propagation affects the radius of curvature of the Gaussian beam.
9. Select the correct answer that properly fills the gaps. The depth of focus of a Gaussian beam is proportional to the ___________ and inversely proportional to the ___________.
a. wavelength, area of the beam
b. area of the beam, wavelength
c. area of the beam, complex amplitude
d. wavelength, complex amplitude
10. Given a Gaussian beam whose beam waist is 797.88 nm and its radius of curvature at 4 µm is 10.25 µm, what is its wavelength λ?
a. 400 nm
b. 450 nm
c. 500 nm
11. Fill the gap. For distances z>>z0, a Gaussian beam can be approximated by a cone that contains _____ of the beam’s power.
a. 66%
b. 86%
c. 96%
12. If a Gaussian beam propagates a distance f until it meets a lens of focal length f and then propagates a distance f again, what is the new q number of the Gaussian beam in relation to the original Gaussian beam?
a. -q
b. -2f/q
c. -f2/q
13. Yes/No. A Gaussian beam propagates a distance of d1= 10 cm along the positive z-axis until it gets refracted by a concave/diverging lens of focal length equal to 15 cm. Later, the resultant Gaussian beam propagates a distance of d2 = 20 cm until it gets refracted again by a convex/converging lens of focal length 20 cm. Is the beam waist of the Gaussian beam affected?
a. Yes
b. No