4.a). A beam of bright red light of wavelength 654 nm passes through a diffraction grating.Enclosing the space beyond the grating is a large semi-cylindrical screen centered on the grating, with its axis parallel to the slits in the grating. Fifteen bright spots appear on the screen. Find (a) the maximum and (b) the minimum possible values for the slit separation in the diffraction grating.b). An unpolarized beam of light is incident on a stack of ideal polarizing filters. The axis of thefirst filter is perpendicular to the axis of the last filter in the stack. Find the fraction bywhich the transmitted beam’s intensity is reduced in the three following cases. (a) Threefilters are in the stack, each with its transmission axis at 45° relative to the preceding filter.(b) Four filters are in the stack, each with its transmission axis at 30° relative to thepreceding filter. (c) Seven filters are in the stack, each with its transmission axis at 15°relative to the preceding filter. (d) Comment on comparing the answers to parts (a), (b), and(c). CO3: Solve problems in the area of diffraction & polarization4. a). A beam of bright red light of wavelength 654 nm passes through a diffraction grating.Enclosing the space beyond the grating is a large semi cylindrical screen centered on thegrating, with its axis parallel to the slits in the grating. Fifteen bright spots appear on thescreen. Find (a) the maximum and (b) the minimum possible values for the slit separation inthe diffraction grating.b). An unpolarized beam of light is incident on a stack of ideal polarizing filters. The axis of thefirst filter is perpendicular to the axis of the last filter in the stack. Find the fraction bywhich the transmitted beam's intensity is reduced in the three following cases. (a) Threefilters are in the stack, each with its transmission axis at 45° relative to the preceding filter.(b) Four filters are in the stack, each with its transmission axis at 30° relative to thepreceding filter. (c) Seven filters are in the stack, each with its transmission axis at 15°relative to the preceding filter. (d) Comment on comparing the answers to parts (a), (b), and(c).

Answered: CO3: Solve problems in the area of…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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a). A beam of bright red light of wavelength 654 nm passes through a diffraction grating.
Enclosing the space beyond the grating is a large semi-cylindrical screen centered on the grating, with its axis parallel to the slits in the grating. Fifteen bright spots appear on the screen. Find (a) the maximum and (b) the minimum possible values for the slit separation in the diffraction grating.

b). An unpolarized beam of light is incident on a stack of ideal polarizing filters. The axis of the
first filter is perpendicular to the axis of the last filter in the stack. Find the fraction by
which the transmitted beam’s intensity is reduced in the three following cases. (a) Three
filters are in the stack, each with its transmission axis at 45° relative to the preceding filter.
(b) Four filters are in the stack, each with its transmission axis at 30° relative to the
preceding filter. (c) Seven filters are in the stack, each with its transmission axis at 15°
relative to the preceding filter. (d) Comment on comparing the answers to parts (a), (b), and
(c).

CO3: Solve problems in the area of diffraction & polarization
4. a). A beam of bright red light of wavelength 654 nm passes through a diffraction grating.
Enclosing the space beyond the grating is a large semi cylindrical screen centered on the
grating, with its axis parallel to the slits in the grating. Fifteen bright spots appear on the
screen. Find (a) the maximum and (b) the minimum possible values for the slit separation in
the diffraction grating.
b). An unpolarized beam of light is incident on a stack of ideal polarizing filters. The axis of the
first filter is perpendicular to the axis of the last filter in the stack. Find the fraction by
which the transmitted beam's intensity is reduced in the three following cases. (a) Three
filters are in the stack, each with its transmission axis at 45° relative to the preceding filter.
(b) Four filters are in the stack, each with its transmission axis at 30° relative to the
preceding filter. (c) Seven filters are in the stack, each with its transmission axis at 15°
relative to the preceding filter. (d) Comment on comparing the answers to parts (a), (b), and
(c).

Expert Solution

Step 1

Ans(a)

Conditions for maxima in interference pattern

$d \sin θ_{b r i g h t} = m λ \sin θ_{b r i g h t} = \frac{m λ}{d} \sin θ_{b r i g h t} = \leq 1 \frac{m λ}{d} < 1$

Fifteen spots hence maximum possible slit separation, m=7

$d = 7 λ = 7 (654 n m) = 4.578 μ m$

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