35.33. The walls of a soap bubble have about the same index...

35.33. The walls of a soap bubble have about the same index of refraction as that of plain water, $n=1.33$ . There is air both inside and outside the bubble. (a) What wavelength (in air) of visible light is most strongly reflected from a point on a soap bubble where its wall is 290 $\mathrm{nm}$ thick? To what color does this correspond (see Fig. 32.4 and Table 32.1$) ?(\text { b) Repeat part (a) for a wall thick- } ness of 340 $\mathrm{nm}$ .

Key Concepts

Optical Path Difference

The optical path difference is the extra distance that light travels in the film relative to the light that reflects from the first surface. It is calculated as twice the product of the film's physical thickness and its refractive index. This value, when compared to the wavelength of the incident light (with adjustments for phase shifts due to reflection), determines the specific wavelengths that undergo constructive interference and thus are most strongly reflected.

Thin Film Interference

Thin film interference is a phenomenon where light waves reflected from the top and bottom surfaces of a thin film combine to produce a pattern of constructive or destructive interference. This interference depends on the optical path difference, which is a function of the film's thickness, its index of refraction, and the wavelength of light. This is the underlying principle used to explain the vibrant colors seen in soap bubbles and oil slicks.

Phase Change upon Reflection

When a light wave reflects off a boundary between two media, it may undergo a phase change. Specifically, if the reflection happens from a medium of lower refractive index to a medium of higher refractive index, a half-wavelength (or ? radian) phase shift occurs. Conversely, if light reflects from a higher to a lower index medium, no phase shift occurs. This phase change is crucial for accurately predicting the conditions for constructive interference in thin films.

Transcript

00:01 Hello everyone here it is given the walls of a soap bubble have about the same thickness and reflective index as that of plain water its value is given 1 .33 there is air both inside and outside of the bubble in the part a we have to find wavelength of visual light is most strongly reflected most strongly reflected that we have to find if thickness of wall of the soap is 290 nanometer in b part we have to find the same for thickness 340 nanometer let us see here since the reflex is producing the face difference of 180 degree so for constructive interference part difference 2t must be m plus half lambda so for constructive interference part difference 2t must be m plus half lambda not by n more most strongly reflected means the wavelength of light for which constructive interference is taking place that you should keep in mind so from here you will find lambda knot to be 2n into t divided by m plus half now substitute the value to n is given 1 .33 part a for part a thickness is 290 nanometer divided by m plus half so lambda not you will get 7 7 .4 7 -7 nanometer divided by m plus half.

03:11 Now we can put the value of m, m is equal to 0 and so on.

03:21 So from here we can write for m is equal to 0 lambda not will be 1543 nanometer which is not visible for m is equal to 1 it would be 1.

03:48 Be 514 meter for m is called to 2 you have to keep on substituting the value here it becomes 308 nanometer and so on you can find but since we have to find the wavelength only in visible region so only this value is correct so the light which is strongly refracted having the wavelength 514 nanometer here i have to write the unit correctly that is nanometer.

04:40 So this is the correct answer of part a.

04:45 Now part b for thickness...

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