Problem 3 - Physics

Question

A plate glass window \((n=1.5)\) has a thickness of \(4.0 \times 10^{-3} \mathrm{~m}\). How long does it take light to pass perpendicularly through the plate?

Step-by-Step Solution

Answer

The time is \(2.0 \times 10^{-11}\) seconds.

Step 1: Identify Given Values

We know that the refractive index of the glass, denoted as \(n\), is 1.5. The thickness of the glass \(d\) is \(4.0 \times 10^{-3}\) meters. We need to find the time \(t\) it takes for light to pass through the glass.

Step 2: Determine the Speed of Light in Glass

The speed of light in a medium \(v\) can be calculated using the equation:\[v = \frac{c}{n}\]where \(c\) is the speed of light in a vacuum \((3.0 \times 10^8 \text{ m/s})\). Substitute the given value of \(n\):\[v = \frac{3.0 \times 10^8 \text{ m/s}}{1.5} = 2.0 \times 10^8 \text{ m/s}\]

Step 3: Calculate Time Taken Using Speed and Distance

To find the time \(t\) it takes for light to travel through the glass, use the formula:\[t = \frac{d}{v}\]Substitute the values of \(d\) and \(v\):\[t = \frac{4.0 \times 10^{-3} \text{ m}}{2.0 \times 10^8 \text{ m/s}} = 2.0 \times 10^{-11} \text{ s}\]

Step 4: Conclusion

The time taken for light to pass perpendicularly through the glass plate is \(2.0 \times 10^{-11}\) seconds.

Key Concepts

Speed of Light

The speed of light, denoted by the symbol \(c\), is a fundamental constant of nature. In a vacuum, light travels at a speed of approximately \(3.0 \times 10^8\) meters per second. This speed is incredibly fast. It allows light to cover vast distances in short periods of time.

The importance of the speed of light extends beyond just understanding how light travels. It is a crucial component in many scientific equations and theories, such as Einstein's theory of relativity. In our everyday world, knowing the speed of light helps us calculate how long it takes light to travel through different materials, which is invaluable in optics.

• In a vacuum, light travels at \(3.0 \times 10^8\) m/s.
• The speed changes when light enters different materials.
• The calculation of light's speed in mediums is critical in technology and science.

Refractive Index

The refractive index, often represented by \(n\), is a measure of how much a substance slows down light. When light transitions from one medium to another, such as from air to glass, it changes speed due to the refractive index of the new medium.

The refractive index is calculated using the formula \(n = \frac{c}{v}\), where \(c\) is the speed of light in a vacuum, and \(v\) is the speed of light in the medium. A higher refractive index indicates the medium slows light more. For example, glass with \(n = 1.5\) reduces the speed of light compared to air, which has a refractive index close to 1.

• Glass with \(n = 1.5\) slows light to \(2.0 \times 10^8\) m/s.
• Refractive index is a dimensionless number.
• It helps determine how much light bends when entering a different medium.

Medium

A medium is any material through which light can travel. Common mediums include air, water, and glass. Each medium has unique properties that affect the speed and direction of light passing through it.

The optical properties of a medium are largely dependent on its refractive index. When light enters a medium with a different refractive index, its speed and direction change, which can be observed as refraction. This change is essential in designing lenses and other optical devices.

• Light travels slower in a denser medium.
• Understanding mediums is crucial for optics and various technologies.
• Changes in speed and direction of light in a medium are due to refraction.