Chapter 16, Problem 42A

To determine

To Find:The distance of the mirror from the person.

Answer to Problem 42A

The distance of the mirror from the person is $\text{15,000 km}$ .

Explanation of Solution

Given:

The time interval between the person and mirror is $0.1\text{s}$ .

Formula Used:

The minimum distance of the image from the object is

  ${\text{d}}_{\text{min}}=\text{c}\left(\frac{{\text{t}}_{\text{min}}}{2}\right)$.........(1)

Here ${\text{t}}_{\text{min}}$ is the minimum time interval that can detect by the person.

Calculation:

The given time interval between the person and mirror is $0.1\text{s}$ .

Substitute $3\times {10}^8\text{ m/s}$ for c and $0.1\text{s}$ for ${\text{t}}_{\text{min}}$ in equation (1)

  $\begin{array}{c}{\text{d}}_{\min }=3\times {10}^8 \text{m/s}\left(\frac{\text{0}\text{.1 s}}{\text{2}}\right)\\ \text{}{\text{d}}_{\min }= 1.5\times {10}^7 \text{m}\left(\frac{\text{1 km}}{{\text{10}}^{\text{3}}\text{ m}}\right)\text{}\\ {\text{d}}_{\text{min}}\text{= 15,000 km}\end{array}$

Diameter of earth is $\text{12,742}\text{km}$ . The distance between the mirror and the person is larger than the diameter of the earth.

Conclusion:

Hence, the required minimum distance of the mirror is $\text{15,000 km}$ .