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1Optics Practice Quiz 3
1. Advanced students only Consider the paraxial wave equation
for a uniformmedium with refractive index nm.
(a) For this medium we have we have to take k appearing in the
paraxial waveequation as k = km where km = nm/c.
(b) For this medium we can take k appearing in the paraxial wave
equation ask = nm/c, but we do not have to, provided that k and km
are close.
(c) For this medium we can take k appearing in the paraxial wave
equation to bearbitrary.
(d) In the paraxial wave equation k is the wavenumber in
vacuum.
2. Advanced students only Which of the following statements is
incorrect?
(a) The use of the paraxial wave equation implies a preferred
direction has beenchosen.
(b) The paraxial wave equation is an equation for a scalar
field
(c) The paraxial cannot accurately describe beams which have a
waste whichsmaller than the wavelength of the light.
(d) The k which appears in the paraxial wave equation is the
wave number invacuum
3. Consider the equation
U(Qx, Qy, z) = U(Qx, Qy, 0) ei(Q2x+Q2y)z/(2k),Which of the
statements below is correct?
(a) The equation expresses that the field propagates like a
plane wave with a com-plicated wavenumber.
(b) The equation expresses that the Fourier transform of the
field propagates likea plane wave with a complicated
wavenumber.
(c) The equation expresses that the Fourier transform of the
field propagates inthe z direction like a plane wave with a
complicated wavenumber.
(d) The equation solves the paraxial wave equation in terms of
the Fourier trans-form of the field
4. In the equation w20 w20 + 2iz/k, what is/are the
consequence(s) of the last termon the right-hand side?
(i.) It directly leads to a change in the peak value of the
Gaussian beam with z.
(ii.) It directly leads to a change in the curvature of the
phase fronts of a Gaussianbeam
(iii.) It directly leads to a change in the spot size of a
Gaussian beam
How many of these three statements are correct?
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2(a) They are all incorrect
(b) Only one is correct
(c) Two are correct
(d) All three are correct
5. The result
=2
kw0
refers to the following property of a Gaussian beam
(a) The angle of incidence in a medium
(b) The asymptotic half-angle over which the Gaussian beam
diverges
(c) The asymptotic full angle over which a Gaussian beam
diverges
(d) The angle between the direction of the beam and the electric
field.
6. Compare two Gaussian beams with the same beam waist, but one
propagating inair with n = 1 (Beam I), and the other in water with
n = 1.33 (Beam II).
Which of the following statements is true?
(a) The propagation of the two beams is identical.
(b) Beam I diffracts faster than Beam II in the far field.
(c) Beam II diffracts faster than Beam I in the far field
(d) The beams propagate differently but diffract at the same
rate in the far field
7. Consider the equation:
w0 =w
1 +(kw2
2
)2 ,and the two statements:
(i.) This equation gives the value of the beam waist given the
width and the wavefront curvature at some position.
(ii.) This equation gives the value of the beam waist given the
width of the beamat some position and the wavefront curvature at
another position.
Which of these statements is correct?
(a) Both statements are correct.
(b) Statement (i.) is correct but statement (ii.) is not.
(c) Statement (ii.) is correct but statement (i.) is not.
(d) Both statements are incorrect.
8. The expression w1 = w2 would refer to:
(i.) The situation in which a Gaussian beam is focused or
defocused by a lens.
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3(ii.) The situation in which a Gaussian beam is focused or
defocused by a curvedmirror
(iii.) The situation in which a Gaussian beam enters a medium
with a differentrefractive index.
How many of these three statements are correct?
(a) They are all incorrect
(b) Only one is correct
(c) Two are correct
(d) All three are correct
9. The focal shift (a) is wavelength independent(b) increases
with increasing wavelength(c) decreases with increasing
wavelength(d) can either decrease or increase with increasing
wavelength
