3. (5 pts.) Suppose that a shiny silver spherical Christmas-tree ornament makes

Question

3. (5 pts.) Suppose that a shiny silver spherical Christmas-tree ornament makes a nicely reflective convex mirror. The ornament has a diameter of 10.0 cm. You position your face (the "object") 6.0 cm away from the surface of the ornament. When you look at the ornament, you see your reflection (the "image"). What is the magnification of your reflection? Is it upright or inverted? Show your work completely 4. (5 pts.) You notice a thin layer of transparent oil floating on the surface of a water puddle. Suppose that sunlight strikes the puddle from nearly directly overhead, and also that you are viewing the puddle from nearly directly above the puddle. You see bright colored light reflected from the oil, and the color gradually varies as the oil's thickness varies. In one particular region, the oil appears to be bright green aar-550. nm). If nol-1.50 and nwater= 1.33. how thick (in nanometers) is the oil layer in that region? Since there are an infinite number of solutions, give the three thinnest answers. Show your work clearly, and include a sketch if desired.

Explanation / Answer

3] The focal length of the convex mirror will be:

f = - R/2

where R is the radius of the curvature.

=> f = - (10/2)/2 = - 2.5 cm

use the mirror equation

1/f = 1/v + 1/u

=> - 1/2.5 = 1/v + 1/6

=> v = - 1.7647 cm

therefore, the magnification of the image will be:

m = - v/u = - (-1.7647)/6 = +0.294

The image will be upright and virtual in nature.

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