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Chapter 35: Q102P (page 1080)

In a phasor diagram for any point on the viewing screen for the two slit experiment in Fig 35-10, the resultant wave phasor rotates60.0°in 2.50×10-16 s. What is the wavelength?

Short Answer

Expert verified

Thus, the wavelength of light is 450nm.

Step by step solution

01

According to the question.

It is given that

Δϕ=60°=π3rad

The figure according to the question is:

The phasors rotate with constant angular velocity

ω=ΔϕΔt=π3×2.5×10-16 s=4.19×1015 rad/s

02

The wavelength of light in medium. 

Since, light waves travelling in a medium (air) where the wave speed is approximately c, then kc=ω,wherek=2πλ, which leads to

λ=2πcω=2π×3×108m/s4.19×1015rad/s=4.498×10-7m=450nm

Hence, the wavelength of light is, 450nm.

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Most popular questions from this chapter

In a double-slit experiment, the fourth-order maximum for a wavelength of 450 nm occurs at an angle of θ=90°. (a) What range of wavelengths in the visible range (400 nm to 700 nm) are not present in the third-order maxima? To eliminate all visible light in the fourth-order maximum, (b) should the slit separation be increased or decreased and (c) what least change is needed?

The rhinestones in costume jewellery are glass with index of refraction 1.50. To make them more reflective, they are often coated with a layer of silicon monoxide of index of refraction 2.00.What is the minimum coating thickness needed to ensure that light of wavelength 560nm and of perpendicular incidence will be reflected from the two surfaces of the coating with fully constructive interference?

How much faster, in meters per second, does light travel in sapphire than in diamond? See Table 33-1.

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 ray r3 (the light does not reflect inside material 2) and r4(the light reflects twice inside material 2). The waves of r3 and r4 interfere, 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,n2andn3, the type.

Of interference, the thin-layer thickness L in nanometres, and the wavelength λ in nanometres of the light as measured in air.

Where λ is 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?

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?
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