Lead glass, which is commonly called “crystal”, contains about 24% PbO and has a

Question

Lead glass, which is commonly called “crystal”, contains about 24% PbO and has an index of refraction of ncrystal= 2.0. An unknown liquid is placed between two parallel lead glass plates. When the separation between the plates, t, is set to 560 nm, it is found that light with a wavelength equal to 660 nm in air is canceled out by thin film interference. What is the index of refraction, nliquid, of the liquid? (Hint: indices of refraction for liquids range from 1.3 to 1.9).

Can you also please explain how to determine phase changes.

Explanation / Answer

Since ncrystal> nliquid, the wave reflecting from the upper crystal-liquid boundary will have no phase change, whereas the wave reflecting from the lower crystal-liquid boundary will have a 180o phase shift.

So, for destructive interference,

2nliquidt = m

=> nliquid = m/2t = m * 660 / (2 * 560) = 33m/56

Now, 1.3 < nliquid < 1.9

For m = 1, nliquid = 33 * 1 / 56 = 0.6

For m = 2, nliquid = 33 * 2 / 56 = 1.2

For m = 3, nliquid = 33 * 3 / 56 = 1.8

Since 1.8 lies between 1.3 and 1.9,

nliquid = 1.8

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.