Thickness of Film:Constructive Interference @ 547nm, n=1.31

In summary, the thickness of a film is crucial in determining whether constructive interference will occur at 547nm, with an equal thickness to the wavelength resulting in constructive interference and a darker appearance otherwise. The refractive index of the film also plays a key role, with a higher index requiring a thicker film for constructive interference. 547nm is a significant wavelength due to its place in the visible spectrum and its use in scientific research. Other factors such as angle of incidence, polarization, and surface quality can affect constructive interference. This phenomenon is used in practical applications such as thin film production and optical instruments for measuring materials.
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Homework Statement


Light of wavelength 547nm is incident perpendicularly on a soap film (n=1.31) suspended in air. What is the smallest nonzero film thickness for which reflected light undergoes constructive interference?

Homework Equations


2t = (m + 1/2)(wavelength/nfilm)

The Attempt at a Solution


t = (0+1/2)(547nm/(2*1.31))
t = 104 nm

Is this correct?---------
Could someone please check this as well: https://www.physicsforums.com/showthread.php?t=310439
 
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Anyone?
 
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It is correct.
 

FAQ: Thickness of Film:Constructive Interference @ 547nm, n=1.31

What is the significance of the film's thickness when it comes to constructive interference at 547nm?

The thickness of a film is crucial in determining whether constructive interference will occur at a specific wavelength, in this case 547nm. If the thickness is equal to an integer multiple of the wavelength, then there will be constructive interference and the film will appear bright. If not, then there will be destructive interference and the film will appear dark.

How does the refractive index of the film affect constructive interference at 547nm?

The refractive index of the film, which is a measure of how much light is bent as it passes through the film, plays a key role in determining the thickness needed for constructive interference at 547nm. A higher refractive index means that the light will travel slower through the film, resulting in a thicker film needed for constructive interference.

Why is 547nm a significant wavelength in the study of constructive interference?

547nm is a significant wavelength because it falls within the visible spectrum, which is the range of wavelengths that can be seen by the human eye. It is also a commonly used wavelength in scientific research and is often used as a reference point in experiments involving constructive interference.

What other factors besides film thickness and refractive index can affect constructive interference at 547nm?

Other factors that can affect constructive interference at 547nm include the angle of incidence of the light, the polarization of the light, and the quality of the film's surface. These factors can alter the path of the light and change the conditions for constructive interference.

How is constructive interference at 547nm used in practical applications?

Constructive interference at 547nm has various practical applications, such as in the production of thin films for optical coatings and the creation of colorful patterns in soap bubbles and oil slicks. It is also used in various optical instruments, such as interferometers and spectrometers, to measure the thickness and refractive index of materials.

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