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Chapter 22: Problem 17

How long does it take light to travel from this text to your eyes? Assume a distance of \(50.0 \mathrm{cm}\).

Short Answer

Expert verified
Answer: It takes approximately \(1.7 \times 10^{-9}\) seconds for light to travel from the text to the observer's eyes.

Step by step solution

01

Convert distance to meters

Given distance is 50.0 cm. To convert it into meters, we'll divide it by 100. So, the distance in meters is: \[d = \frac{50.0}{100} \mathrm{m}\]
02

Calculate the time taken

We know that the speed of light (c) is approximately \(3.0\times10^8 \mathrm{m/s}\). To find the time it takes for light to travel this distance, we'll use the formula: \[t = \frac{d}{c}\] Now, plug in the values for d and c: \[t=\frac{50.0/100}{3.0 \times 10^8} \mathrm{seconds}\]
03

Simplify the expression

Now, we have to simplify the expression: \[t=\frac{50.0}{100} \times \frac{1}{3.0 \times 10^8} \mathrm{seconds}\]
04

Calculate the result

Multiply the numbers together: \[t = \frac{50.0}{100} \times \frac{1}{3.0 \times 10^8} = \frac{1}{2} \times \frac{1}{3.0 \times 10^8} \approx \frac{1}{6.0 \times 10^8}\]
05

Express the result in scientific notation

Express the result in scientific notation, keeping one significant figure: \[t \approx 1.7 \times 10^{-9} \mathrm{seconds}\] So, it takes approximately \(1.7 \times 10^{-9}\) seconds for light to travel from the text to the observer's eyes.

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Most popular questions from this chapter

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