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Chapter 35: Q96P (page 1080)

A camera lens with index of refraction greater than 1.30 is coated with a thin transparent film of index of refraction 1.25 to eliminate by interference the reflection of light at wavelength 位 that is incident perpendicularly on the lens. What multiple of 位gives the minimum film thickness needed?

Short Answer

Expert verified

Thus, the minimum film needed is 0.200.

Step by step solution

01

The thin film interference of a coating on glass lens.

The formula for the thin film interference of coating on the glass lens:

Lmin=位4n2

02

The minimum film thickness needed by multiple of .

Use the above formula as follows:

Lmin=位4n2=位41.25=0.200位

Further solve as follows:

Lmin=0.200位Lmin位=0.200

Hence, the minimum film needed is 0.200.

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Most popular questions from this chapter

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 r3andr4interfere, 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 refractionn1,n2andn3the type of interference, the thin-layer thicknessLin nanometers, and the wavelength位in nanometers of the light as measured in air. Where位is missing, give the wavelength that is in the visible range. WhereLis missing, give the second least thickness or the third least thickness as indicated.

In the double-slit experiment of Fig. 35-10, the viewing screen is at distance D=4.00m, point P lies at distance role="math" localid="1663143982922" y=20.5cmfrom the center of the pattern, the slit separation d is 4.50mm, and the wavelength 位is 580 nm. (a) Determine where point P is in the interference pattern by giving the maximum or minimum on which it lies, or the maximum and minimum between which it lies. (b) What is the ratio of the intensitylPat point P to the intensitylcen at the centerof the pattern?

Light of wavelengthis used in a Michelson interferometer. Letx be the position of the movable mirror, withx=0when the arms have equal lengthsd2=d1. Write an expression for the intensity of the observed light as a function of , lettinglmbe the maximum intensity.

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, n2, and n3, the type of interference, the thin-layer thickness L in nanometers, and the wavelength 位 in nanometers of the light as measured in air. Where 位 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.

The figure shows the design of a Texas arcade game, Four laser pistols are pointed toward the center of an array of plastic layers where a clay armadillo is the target. The indexes of refraction of the layers are n1=1.55,n2=1.70,n3=1.45,n4=1.60,n5=1.45,n6=1.61,n7=1.59,n8=1.70and n9=1.60. The layer thicknesses are either 2.00 mm or 4.00 mm, as drawn. What is the travel time through the layers for the laser burst from (a) pistol 1, (b) pistol 2, (c) pistol 3, and (d) pistol 4? (e) If the pistols are fired simultaneously, which laser burst hits the target first?
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