An object surrounded by a translucent material with index of refraction greater than unity appears enlarged. This includes items such as plants or shells inside plastic or resin paperweights, as well as ancient bugs trapped in amber. Consider a spherical object in air with radius r fixed at the center of a sphere with radius R > r with refractive index n, as shown in Fig. When viewed from outside, the spherical object appears to have radius r′ > r. (a) Using right triangles found in the figure, write an expression for sin θa in terms of r and R. (b) Similarly, write an expression for sin θb in terms of r′ and R. (c) Using Snell’s law, derive an expression for r′ in terms of r, R, and n. (d) If the object is a spherical dandelion seed head with diameter 45.0 mm fixed at the center of a solidified resin sphere with radius 80.0 mm and index of refraction 1.53, what diameter will the seed head appear to have when viewed from outside?
Trending now
This is a popular solution!
Step by step
Solved in 8 steps
