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
To determine the answer to this question, we need to understand the concept of thin film interference. When light waves encounter a thin film, some of them are reflected and some are transmitted through the film. The reflected waves can interfere with each other, resulting in constructive or destructive interference.
For constructive interference, the path difference between the reflected waves must be an integer multiple of the wavelength of the light. This path difference is equal to 2 times the thickness of the film when the light reflects off the front and back surfaces of the film.
So, for the strongest color reflected in a thin film, we need to find the condition where the path difference is equal to the wavelength of the color. Based on this information, let's evaluate the options:
a. The thickness: This option states that the strongest color has a wavelength equal to the thickness of the film. This is not correct because the thickness is related to the path difference, not the wavelength.
b. Twice the thickness: This option suggests that the strongest color has a wavelength equal to twice the thickness of the film. This could be the case as constructive interference can occur with a path difference of 2 times the thickness. However, this option is not always true for all colors.
c. Four times the thickness: This option states that the strongest color has a wavelength equal to four times the thickness of the film. This is incorrect because the path difference of 4 times the thickness does not correspond to the wavelengths of the strongest colors.
d. Two or four times the thickness, depending upon the number of wave inversions: This option states that the wavelength of the strongest color can be either 2 times or 4 times the thickness of the film, depending on the number of wave inversions. This is the correct answer because the path difference of 2 times the thickness results in constructive interference for some colors, while the path difference of 4 times the thickness results in constructive interference for other colors, depending on whether there is an even or odd number of wave inversions.
Therefore, the correct answer is option d.