Section   7.1Reflection

1. (Exercises 3 and 4) What is the minimum height for the reflecting portion of a mirror that can be used by a 7-ft 2-in. professional basketball star to see his complete (head-to-toe) image?

This calculation is quite simple because the relationship between the minimum height of the mirror and the height of the person is just a factor of 2 (see Figure 7.4 in the textbook).

H_minimum = Height of person / 2 = 7 ft 2 in. / 2

H_minimum = 3.5 ft 1 in.

H_minimum = 3 ft 7 in.

Section   7.2Reflection and Dispersion

2. (Exercises 7 and 8) Light travels through glass at a speed that is 65% as fast as it travels through vacuum. What is the index of refraction of the glass?

First, we find the speed of light through the glass.

c_glass = c_vacuum (0.65) = 3.00 x 10⁸ m/s (0.65)

c_glass = 1.95 x 10⁸ m/s

Now we can find the index of refraction by using the definition given by Equation 7.1 in the textbook.

n_glass = c_vacuum / c_glass = 3.00 x 10⁸ m/s / 1.95 x 10⁸ m/s

n_glass = 1.54

Comparing this with the values for the index of refraction given in Table 7.1 in the textbook, we find that this is close to but not exactly the same index of refraction as that given for crown glass. The particular composition of glass determines its index of refraction, and this sample is evidently not the type commonly classified as crown glass.

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