Bottles of perfume sometimes have thick glass (n=1.5) walls which give the impre
ID: 2123949 • Letter: B
Question
Bottles of perfume sometimes have thick glass (n=1.5) walls which give the impression the volume is larger than it is. Assume a cylindrical bottle has an inner radius of 1.0cm and an outer radius of 2.0cm. How thick (in cm) would the wall appear if you could see a mark on the inside surface?
I found on another site that the right answer is 0.80cm. I don't know how to get this answer though.. I also read that I should use the formula: (n1/p)+(n2/q)=(n2-n1)/R
I don't know if this is the right formula to use.. Please, help!
Explanation / Answer
The "lens equation" of only one refracting surface: n1/o + n2/i = (n2-n1)/Rwhere
n1 is the refractive of the media which the light is coming from.
n2 is the refractive of the media which the light is going to.
o and i are the object distance and image distance respectively.
R is the radius of curvature of a spherical/circular refractive surface.
Here, we have n1 = 1.5, n2 = 1, o = 2-1 = 1 = the distance of inner surface from the outer surface, R = -2 (-ve as the curvature is away from the object).
Hence the i = 1/[(1-1.5)/-2 - 1.5/1] = -0.8cm
So we see the inner surface is 0.8cm from the outer surface, implying we think the bottle is 0.8cm thick. The -ve sign means the image is virtual.
homepage.smc.edu/kocharian_armen/Physics23/Test%20III%20F.pdf%u200E
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