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Chapter 33: Q. 57 (page 957)

FIGURE P33.56 shows the light intensity on a screen behind a single slit. The wavelength of the light is $600 nm$ and the slit width is $0.15 mm$ . What is the distance from the slit to the screen?

Short Answer

Expert verified

The distance from the slit to the screen $1.25 m$

Step by step solution

01

Central Cringe

Remember that the entire width of a main fringes in the single study is given by

$w_{c} = \frac{2 λ L}{a}$

In an intellectual result, we can resolve parametrically only for the length to find a solution.

$L = \frac{a w_{c}}{2 λ}$

02

Length

In terms of quantity, our length will just be

$L = \frac{1.5 \times 10^{- 4} \cdot 1 \times 10^{- 2}}{2 \cdot 6 \times 10^{- 7}} = 1.25 m$

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Most popular questions from this chapter

To illustrate one of the ideas of holography in a simple way, consider a diffraction grating with slit spacing $d$ . The small-angle approximation is usually not valid for diffraction gratings, because $d$ is only slightly larger than $λ$ , but assume that the $λ / d$ ratio of this grating is small enough to make the small-angle approximation valid.

a. Use the small-angle approximation to find an expression for the fringe spacing on a screen at distance $L$ behind the grating.

b. Rather than a screen, suppose you place a piece of film at distance $L$ behind the grating. The bright fringes will expose the film, but the dark spaces in between will leave the film unexposed. After being developed, the film will be a series of alternating light and dark stripes. What if you were to now “play” the film by using it as a diffraction grating? In other words, what happens if you shine the same laser through the film and look at the film’s diffraction pattern on a screen at the same distance $L$ ? Demonstrate that the film’s diffraction pattern is a reproduction of the original diffraction grating

Light of wavelength $600 n m$ passes though two slits separated by $0.20$ $m m$ and is observed on a screen $1.0 m$ behind the slits. The location of the central maximum is marked on the screen and labeled $y = 0 .$

a. At what distance, on either side of $y = 0$ , are the $m = 1$ bright fringes?

b. A very thin piece of glass is then placed in one slit. Because light travels slower in glass than in air, the wave passing through the glass is delayed by $5.0 \times 10 - 16 s$ in comparison to the wave going through the other slit. What fraction of the period of the light wave is this delay?

c. With the glass in place, what is the phase difference $Δ ϕ_{0}$ between the two waves as they leave the slits? $2$

d. The glass causes the interference fringe pattern on the screen to shift sideways. Which way does the central maximum move (toward or away from the slit with the glass) and by how far?

A double slit is illuminated simultaneously with orange light of wavelength $620 nm$ and light of an unknown wavelength. The $m = 4$ bright fringe of the unknown wavelength overlaps the $m = 3$ bright orange fringe. What is the unknown wavelength $?$

FIGURE shows light of wavelength $λ$ incident at angle $ϕ$ on a reflection grating of spacing $d$ . We want to find the angles um at which constructive interference occurs.

a. The figure shows paths $1$ and $2$ along which two waves travel and interfere. Find an expression for the path-length difference $Δ r = r_{2} - r_{1}$ . $3$ 3

b. Using your result from part a, find an equation (analogous to Equation localid="1650299740348" $(33.15)$ for the angles localid="1650299747450" $θ_{m}$ at which diffraction occurs when the light is incident at angle localid="1650299754268" $\emptyset$ . Notice that m can be a negative integer in your expression, indicating that path localid="1650299766020" $2$ is shorter than path localid="1650299773517" $1$ .

c. Show that the zeroth-order diffraction is simply a “reflection.” That is, localid="1650299781268" $θ_{0} = ϕ$

d. Light of wavelength 500 nm is incident at localid="1650299787850" $ϕ = 40^{\circ}$ on a reflection grating having localid="1650299794954" $700$ reflection lines/mm. Find all angles localid="1650299802944" $θ_{m}$ at which light is diffracted. Negative values of localid="1650299812949" $θ_{m}$
are interpreted as an angle left of the vertical.

e. Draw a picture showing a single localid="1650299823499" $500 n m$ light ray incident at localid="1650299833529" $ϕ = 40^{\circ}$ and showing all the diffracted waves at the correct angles.

$F I G U R E P 33.49$ shows the interference pattern on a screen $1.0 m$ behind an $800 l i n e / m m$ diffraction grating. What is the wavelength (in $m m$ ) of the light?

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