48. The strongest colors reflected in a thin film have wavelengths in the film equal to ____ of the thinnest possible film.
a. the thickness
b. twice the thickness
c. four times the thickness
d. two or four times the thickness, depending upon the number of wave inversions
d or c?
d
c. four times the thickness
To determine the answer to this question, we need to understand the principles behind thin film interference.
When light passes through a thin film, such as a soap bubble or an oil slick, it undergoes two reflections: one from the top surface of the film and another from the bottom surface of the film. These two reflected waves can interfere with each other constructively or destructively, depending on the path difference between them.
The path difference is determined by the thickness of the film and the index of refraction of the medium surrounding the film. When the path difference is a whole number multiple of the wavelength of light, constructive interference occurs, resulting in a bright color being reflected. When the path difference is a half-number multiple of the wavelength, destructive interference occurs, resulting in a dark or no color being reflected.
The condition for constructive interference is given by the formula:
2 * thickness * refractive index = m * wavelength
Here, 'thickness' refers to the thickness of the thin film, 'refractive index' refers to the refractive index of the medium surrounding the film, 'm' is the order of the interference pattern (an integer), and 'wavelength' is the wavelength of light in that medium.
Now back to the question: the strongest colors reflected in a thin film have wavelengths that satisfy the condition for constructive interference, which is given by the equation 2 * thickness * refractive index = m * wavelength.
In this case, we are looking for the wavelength of light in the film that corresponds to the thinnest possible film. Since we have no specific values mentioned for the refractive index or a particular value for 'm', we cannot determine the exact value of the wavelength. Therefore, the answer must be either (c) four times the thickness or (d) two or four times the thickness, depending upon the number of wave inversions.
In thin film interference, the order of the interference pattern can be an integer or a half-integer value. If we assume it is an integer (e.g., m = 1), then the condition for constructive interference becomes:
2 * thickness * refractive index = wavelength
In this case, the strongest colors reflected in the thin film would indeed have wavelengths equal to the thickness of the film (option a). However, if we assume it is a half-integer (e.g., m = 1/2), then the condition for constructive interference becomes:
2 * thickness * refractive index = 2 * wavelength
In this case, the strongest colors reflected in the thin film would have wavelengths equal to twice the thickness of the film (option b). Therefore, the correct answer would be (d) two or four times the thickness, depending upon the number of wave inversions.
In conclusion, the answer to the question is either (c) four times the thickness or (d) two or four times the thickness, depending upon the number of wave inversions.