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A thin film of oil (no = 1.5) with varying thickness floats on water (n = 1.33). When it is illuminated from above by white light, the reflected colors are as shown in the figure. In air, the wavelength of yellow light is Ayellow = 580 nm. Dark (1) Why are there no reflected colors at point A? (2) What is the oil's thickness at point B? Blue Yellow Red anig Yellow B Air Oil no = 1.5 Water nw=1.33

A thin film of oil (no = 1.5) with varying thickness floats on water (n = 1.33). When it is illuminated from above by white light, the reflected colors are as shown in the figure. In air, the wavelength of yellow light is Ayellow = 580 nm. Dark (1) Why are there no reflected colors at point A? (2) What is the oil's thickness at point B? Blue Yellow Red anig Yellow B Air Oil no = 1.5 Water nw=1.33

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A thin film of oil (\(n_o = 1.5\)) with varying thickness floats on water (\(n_w = 1.33\)). When it is illuminated from above by white light, the reflected colors are as shown in the figure. In air, the wavelength of yellow light is \(\lambda_{\text{yellow}} = 580 \text{ nm}\). (1) Why are there no reflected colors at point A? (2) What is the oil’s thickness at point B? ### Diagram Explanation The diagram shows a cross-sectional view of a thin film of oil floating on water. Above the oil is air. The oil has a refractive index \(n_o = 1.5\), and the water beneath it has a refractive index \(n_w = 1.33\). The oil film shows varying colors due to interference effects. At point A, the region is labeled as "Dark," indicating no color is reflected. Moving from A to B, colors change: - A is labeled as dark. - Near A, a sequence of colors is labeled from left to right as "Blue," "Yellow," "Red," "Blue," "Yellow." This variation in color is due to constructive and destructive interference at different thicknesses of the oil film, depending on the wavelength of light in air (\(\lambda_{\text{yellow}} = 580 \text{ nm}\)). When the path difference causes destructive interference for all visible wavelengths, the region appears dark, as at point A. Different colors appear at other points due to constructive interference for specific wavelengths.
Transcribed Image Text:A thin film of oil (\(n_o = 1.5\)) with varying thickness floats on water (\(n_w = 1.33\)). When it is illuminated from above by white light, the reflected colors are as shown in the figure. In air, the wavelength of yellow light is \(\lambda_{\text{yellow}} = 580 \text{ nm}\). (1) Why are there no reflected colors at point A? (2) What is the oil’s thickness at point B? ### Diagram Explanation The diagram shows a cross-sectional view of a thin film of oil floating on water. Above the oil is air. The oil has a refractive index \(n_o = 1.5\), and the water beneath it has a refractive index \(n_w = 1.33\). The oil film shows varying colors due to interference effects. At point A, the region is labeled as "Dark," indicating no color is reflected. Moving from A to B, colors change: - A is labeled as dark. - Near A, a sequence of colors is labeled from left to right as "Blue," "Yellow," "Red," "Blue," "Yellow." This variation in color is due to constructive and destructive interference at different thicknesses of the oil film, depending on the wavelength of light in air (\(\lambda_{\text{yellow}} = 580 \text{ nm}\)). When the path difference causes destructive interference for all visible wavelengths, the region appears dark, as at point A. Different colors appear at other points due to constructive interference for specific wavelengths.
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