Question
9. (4) Benzene gas has an optical density of 1.001762. A distant planet has an atmosphere made of benzene. How much time would it take for a ray of light to travel a distance of 7890km in its almosphere?
Solution
4.6
(187 Votes)
Norris
Master · Tutor for 5 years
Answer
Here's how to calculate the time it takes for light to travel through the benzene atmosphere:**1. Understand the relationship between optical density, refractive index, and the speed of light:*** **Optical Density:** While sometimes used loosely, optical density usually refers to absorbance, or how much light is absorbed by a medium. It's *not* directly used to calculate light's speed. The question likely meant to say **refractive index**.* **Refractive Index (n):** This is the ratio of the speed of light in a vacuum (c) to the speed of light in the medium (v). n = c/v* **Speed of Light in a Vacuum (c):** Approximately 3 x 10^8 meters/second.**2. Calculate the speed of light in the benzene atmosphere:*** Given refractive index (n) = 1.001762* v = c / n* v = (3 x 10^8 m/s) / 1.001762* v ≈ 2.9948 x 10^8 m/s**3. Convert the distance to meters:*** Distance = 7890 km = 7890 * 1000 m = 7.89 x 10^6 m**4. Calculate the time:*** Time = Distance / Speed* Time = (7.89 x 10^6 m) / (2.9948 x 10^8 m/s)* Time ≈ 0.02635 seconds**Answer:** It would take approximately 0.02635 seconds for light to travel 7890 km through the benzene atmosphere.