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Chapter 35: Q11Q (page 1073)

Figure 35-28 shows four situations in which light reflects perpendicularly from a thin film of thickness L sandwiched between much thicker materials. The indexes of refraction are given. In which situations does Eq. 35-36 correspond to the reflections yielding maxima (that is, a bright film).

Short Answer

Expert verified

The situation corresponding to the reflections yielding maxima is (c).

Step by step solution

01

Given information:

The thickness of the thin film for each situation is L.

The index of refraction of the thin film for situation (a) is 1.6.

The index of refraction of the thin film for situation (b) is 1.6.

The index of refraction of the thin film for situation (c) is 1.3.

The index of refraction of the thin film for situation (d) is 1.6.

02

Path length difference: 

If two different waves exactly in phase meet each other then they produce fully constructive interference having a bright film.

The formula for the path length difference (2L) of the light in the medium is given by,

2L=m+12位n2

Here, 位 is the wavelength of the incident light, n2 is the index of refraction of the medium, and m=0,1,2...... for maxima-bright film in air.

03

Situation yielding maxima: 

According to the equation 35-36,

2L=m+12位n2

For a particular order, the maximum intensity will be possible when,

2L鈭�1n2

From the above relation, the reflections yield maxima for a medium having the least value of the index of refraction.

Comparing the given four situations,

1.3<1.6

So, the value of the index of refraction is the least for situation (c).

Hence, the situation corresponding to the reflections yielding maxima (that is, a bright film) is (c).

Hence, the situation corresponding to the reflections yielding maxima (that is, a bright film) is (c).

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Most popular questions from this chapter

In Fig. 35-39, two isotropic point sources S1 and S2 emit light in phase at wavelength 位 and at the same amplitude. The sources are separated by distance 2d=6位. They lie on an axis that is parallel to an x axis, which runs along a viewing screen at distance D=20.0位. The origin lies on the perpendicular bisector between the sources. The figure shows two rays reaching point P on the screen, at positionxP. (a) At what value of xPdo the rays have the minimum possible phase difference? (b) What multiple of位 gives that minimum phase difference? (c) At what value ofxPdo the rays have the maximum possible phase difference? What multiple of 位 gives (d) that maximum phase difference and (e) the phase difference when xP=6位 ? (f) When xP=6位, is the resulting intensity at point P maximum, minimum, intermediate but closer to maximum, or intermediate but closer to minimum?

In the two-slit experiment of Fig.35-10, let angle 胃be 20.00C, the slit separation be 4.24渭m, and the wavelength be 位=500nm. (a) What multiple of 位gives the phase difference between the waves of rays r1and r2when they arrive at point Pon the distant screen? (b) What is the phase difference in radians? (c) Determine where in the interference pattern point P lies by giving the maximum or minimum on which it lies, or the maximum and minimum between which it lies?

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.

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?

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?
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