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Chapter 35: Q101P (page 1080)

Find the slit separation of a double-slit arrangement that will produce interference fringes0.018 radapart on a distant screen when the light has wavelengthλ=589 nm.

Short Answer

Expert verified

Thus, the wavelength of visible light is33μm.

Step by step solution

01

According to the question.

In the case of a distant screen the angle θis close to zero so sinθ≈θ

Thus, solve further gives:

Δθ≈Δsinθ=Δmλd=λdΔmΔθ=λd

Here,λ is wavelength of light in air/vacuum.

02

The wavelength of visible light. 

Use the above formula as follows:

d=λΔθ=589×10-9m0.018rad=3.3×10-5m=33μm

Hence, the wavelength of visible light is33μm.

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Most popular questions from this chapter

A double-slit arrangement produces interference fringes for sodium light(λ=589nm)that are 0.200Capart. What is the angular separation if the arrangement is immersed in water (n=1.33)?

Transmission through thin layers. In Fig. 35-43, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) Part of the light ends up in material 3 as rayr3(the light does not reflect inside material 2) andr4(the light reflects twice inside material 2). The waves ofr3and r4interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). For this situation, each problem in Table 35-3 refers to the indexes of refraction n1,n2and n3the type of interference, the thin-layer thickness Lin nanometers, and the wavelength λin nanometers of the light as measured in air. Whereλis missing, give the wavelength that is in the visible range. Where Lis missing, give the second least thickness or the third least thickness as indicated.

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 ?

A 600nm-thick soap film n=1.40in air is illuminated with white light in a direction perpendicular to the film. For how many different wavelengths in the 300to 700nm range is there (a) fully constructive interference and (b) fully destructive interference in the reflected light?

In Fig. 35-4, assume that two waves of light in air, of wavelength 400nm, are initially in phase. One travels through a glass layer of index of refraction n1=1.60and thickness L. The other travels through an equally thick plastic layer of index of refraction n2=1.50. (a) What is the smallest value Lshould have if the waves are to end up with a phase difference of 5.65 rad? (b) If the waves arrive at some common point with the same amplitude, is their interference fully constructive, fully destructive, intermediate but closer to fully constructive, or intermediate but closer to fully destructive?
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