Question

A thin film of oil (n. =1.50) with varying thickness floats on water (nw = 1.33). When it is illuminated from above by white light, the reflected colors are as shown in the figure below. In air, the wavelength of yellow light is 580 nm. (a) What is the oil's thickness t at point B? (hint: this is the second thinnest region for yellow light]. (b) Estimate (no calculation) the oil's thickness at point A. [hint : use the result of part (a) and the figure]. (c) Prove that there are no reflected colors can be seen at point A. (hint: calculate the wavelength to be strongly reflected (constructive interference)at point A). Air Yellow Yellow Red Blue Blue - Dark Oil no = 1.50 В Water nw = 1.33 2014 Pearson Education, Inc.

Answer 1

A problem on interference of light due to reflections from interfaces in a system comprising of oil floating over water.

(a) Wavelength of yellow light in oil 2 580nm z 580nm 2386.7 nm As there is abrupt phase change of IT for reflection from air oil interface and no such phase change for reflection from oil-water interface There hare teer constructive interference of yellow light due to reflection from interfaces, even multiple of t = 2t I 2 - 2 on 2tz odd multiple of op 2+2 (26+1) + where p 2 0, 1, 2, 3 .. on t 2 (2p+1) .... u At B there is second thinnest region giving constructive interference of yellow 2 light ... tz 37 = 3 x 386.7 nm en pal) 2 2900 nm (An () Estimate of oil's thickness at a Z 1/5 times of t I 58 nm (c) For constructive interference at A 58nm=(2+1) A ( Using (1) Forran maximum value of topzo ..on & 258nm on az 232 nm

This is wave length in oil, Corresponding wavelength in air 2 not a 15.00 232 nm 2 348 nm Minimum value of wavelength of visible light is 380 nm which is larger than the maximum wavelength a required for constructive interference using the it region A. Therefore, no reflected colour will be seen at the said region,