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Chapter 33: Q. 49 (page 957)

FIGUREP33.49shows the interference pattern on a screen 1.0mbehind an 800line/mmdiffraction grating. What is the wavelength (in mm) of the light?

Short Answer

Expert verified

The wavelength's light isλ=500nm.

Step by step solution

01

Step: 1 Interference pattern:

When parallel plane waves of the same frequency meet at an angle, a simple sort of interference pattern results. Interference is fundamentally a process of energy redistribution. The energy wasted during destructive interference is recovered during positive interference.

02

Step: 2 Equating equation:

The angle of fringes as

Y1=Ltan⁡θ1θ1=tan−1⁡Y1L

Equation of grating wavelength is

localid="1649148192850" dsin⁡θ1=λ=1×10−3800sin⁡tan−1⁡Y1L

03

Step: 3 Obtaining wavelength:

The wavelength to be

λ=1×10−3800sin⁡tan−1⁡0.4361λ=1.25×10−6sin⁡23.56∘λ=5.00×10−7mλ=500nm.

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Most popular questions from this chapter

3. FIGURE Q33.3 shows the viewing screen in a double-slit experiment. FringeCis the central maximum. What will happen to the fringe spacing if

a. The wavelength of the light is decreased?

b. The spacing between the slits is decreased?

c. The distance to the screen is decreased?

d. Suppose the wavelength of the light islocalid="1649170567955" 500nm. How much farther is it from the dot on the screen in the center of fringe E to the left slit than it is from the dot to the right slit?

A diffraction grating has slit spacing d. Fringes are viewed on a screen at distance L. Find an expression for the wavelength of light that produces a first-order fringe on the viewing screen at distanceLfrom the center of the screen.

A diffraction grating with 600linesmmis illuminated with light of wavelength 510nm. A very wide viewing screen is2.0m behind the grating.
aWhat is the distance between the twom=1 bright fringes?
bHow many bright fringes can be seen on the screen?

A triple-slit experiment consists of three narrow slits, equally spaced by distance dand illuminated by light of wavelength λ. Each slit alone produces intensity I1on the viewing screen at distanceL.
aConsider a point on the distant viewing screen such that the path-length difference between any two adjacent slits isλ. What is the intensity at this point?
bWhat is the intensity at a point where the path-length difference between any two adjacent slits isλ2?

Optical computers require microscopic optical switches to turn signals on and off. One device for doing so, which can be implemented in an integrated circuit, is the Mach-Zender interferometer seen in FIGURE. Light from an on-chip infrared laser (λ=1.000μm)is split into two waves that travel equal distances around the arms of the interferometer. One arm passes through an electro-optic crystal, a transparent material that can change its index of refraction in response to an applied voltage. Suppose both arms are exactly the same length and the crystal’s index of refraction with no applied voltage is1.522.

a. With no voltage applied, is the output bright (switch closed, optical signal passing through) or dark (switch open, no signal)? Explain.

b. What is the first index of refraction of the electro-optic crystal larger than 1.522that changes the optical switch to the state opposite the state you found in part a?
See all solutions

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