Chapter 35, Problem 1P

(a) Does your bathroom mirror show you older or younger than you actually are? (b) Compute an order-of-magnitude estimate for the age difference based on data you specify.

To determine

Whether the bathroom mirror shows a person older or younger than the actual age of the person.

Answer to Problem 1P

The age shown by mirror is less than actual age that is mirror shows the person younger than the actual age.

Explanation of Solution

When rays strike on the face it reflects back and travel toward mirror and then bounce back in just very little second difference. Let consider two events, first when ray leaves the face and second when rays return to the face. Hence, between these two events the person age himself a very few second. Although this time is very less approximately few nanoseconds, but the light that travels between the person and the mirror and does not age at all. So the image in the mirror is actually younger than the person is by few nano-seconds. Hence the person will see him younger than actual age.

Conclusion:

Therefore, mirror shows the person younger than the actually age.

To determine

The order of magnitude estimate for the age difference.

Answer to Problem 1P

order of magnitude estimate for the age difference is ${10}^{-9}\text{s}$.

Explanation of Solution

Formula to calculate time travel by light is,

$t=\frac{2d}{c}$

Here,

$d$ is distance between object and mirror.

$c$ is the speed of light.

Assume distance from the mirror is $40\text{cm}$.

Substitute $40\text{cm}$ for $d$ and $3\times {10}^8\text{m}/\text{s}$ for $c$ in above equation.

$\begin{array}{c}t=\frac{2\times 40\text{cm}}{3\times {10}^8\text{m}/\text{s}}\\ =\frac{2\times 40\text{cm}\frac{{10}^{-2}\text{m}}{1\text{cm}}}{3\times {10}^8\text{m}/\text{s}}\\ =2.67\times {10}^{-9}\text{s}\\ \approx {10}^{-9}\text{s}\end{array}$

Conclusion:

Therefore, order of magnitude estimate for the age difference is ${10}^{-9}\text{s}$.