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Chapter 35: Q93P (page 1079)

If the distance between the first and tenth minima of a double-slit pattern is 18.0 mm and the slits are separated by 0.150 mm with the screen 50.0 cm from the slits, what is the wavelength of the light used?

Short Answer

Expert verified

Thus, the wavelength of light is 600nm.

Step by step solution

01

The separation of slits.

The condition for a minimum in the two-slit interference pattern isdsinθ=(m+12)λ,where dis the slit separation, λis the wavelength,mis an integer, and θis the angle made by the interfering rays with the forward direction. If θis small, sinθmay be approximately byθin radians.

Then, , θ=m+12λdand the distance from the minimum to the central fringe is:

y=Dtanθ≈Dsinθ≈Dθ=m+12Dλd

Where Dis the distance from the slits to the screen. For the first minimumm=0 for the tenth onem=9 . The separation is:

Δy=9+12Dλd-12Dλd=9Dλd

02

Calculate the wavelength of light. 

Solve for the wavelength as follows:

λ=dΔy9D=0.15×10-1m18×10-1m950×10-2m=6.0×10-7m=600nm

Hence, the wavelength of light is 600nm.

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Most popular questions from this chapter

In a double-slit arrangement the slits are separated by a distance equal to 100 times the wavelength of the light passing through the slits. (a)What is the angular separation in radians between the central maximum and an adjacent maximum? (b) What is the distance between these maxima on a screen 50 cm from the slits?

If mirror M2in a Michelson interferometer (fig 35-21) is moved through 0.233mm, a shift of 792 bright fringes occurs. What is the wavelength of the light producing the fringe pattern?

Suppose that Young’s experiment is performed with blue-green light of wavelength 500 nm. The slits are 1.20 mm apart, and the viewing screen is 5.40 m from the slits. How far apart are the bright fringes near the center of the interference pattern?

In Fig. 35-31, a light wave along ray r1reflects once from a mirror and a light wave along ray r2reflects twice from that same mirror and once from a tiny mirror at distance Lfrom the bigger mirror. (Neglect the slight tilt of the rays.) The waves have wavelength λand are initially exactly out of phase. What are the (a) smallest (b) second smallest, and (c) third smallest values of Lλthat result in the final waves being exactly in phase?

If you move from one bright fringe in a two-slit interference pattern to the next one farther out,

(a) does the path length difference ∆Lincrease or decrease and

(b) by how much does it change, in wavelengths λ ?
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