Question

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

Short answer

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

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: \[d = \frac{50.0}{100} \mathrm{m}\]

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: \[t=\frac{50.0/100}{3.0 \times 10^8} \mathrm{seconds}\]

Simplify the expression

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

Calculate the result

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

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.