Snell's law example 2 | Geometric optics | Physics | Khan Academy

TL;DR

This video explains how to calculate the distance traveled by a laser pointer in water using Snell's law and trigonometry.

Transcript

Let's do a slightly more involved Snell's law example. So I have this person over here, sitting at the edge of this pool. And they have a little laser pointer in their hand and they shine their laser pointer. So in their hand, where they shine, it's 1.7 meters above the surface of the pool. And they shine it so it travels 8.1 meters to touch the su... Read More

Key Insights

• ✈️ Snell's law can be used to determine the angles involved in the refraction of light at the interface between two mediums, such as air and water.
• 🗯️ The Pythagorean theorem is useful for finding distances and lengths in right triangles, such as the horizontal distance traveled by the laser pointer.
• 👨‍💼 Trigonometry, including concepts like sine and tangent, can be applied to calculate angles and distances in complex scenarios like this one.
• 🫰 Understanding the relationship between the indices of refraction for different mediums is crucial in applying Snell's law accurately.
• 🛝 Precision and accuracy can be improved by using exact values and rounding only when necessary.
• ❓ Recognizing the relationships between different measurements and using appropriate formulas can simplify complex calculations.
• 🙂 Snell's law can be a useful tool for solving real-world problems involving light and refraction.

Questions & Answers

Q: What is the purpose of using Snell's law in this example?

Snell's law is used to determine the angles involved in the refraction of light as it passes from air to water, which helps calculate the distance traveled by the laser pointer.

Q: How is the distance along the surface of the water calculated?

The distance along the surface is calculated using the Pythagorean theorem, considering the height of the laser pointer above the water and the horizontal distance it travels to touch the water's surface.

Q: How is the angle of refraction determined?

The angle of refraction (theta 2) is calculated by finding the sine of theta 1, which is obtained by dividing the horizontal distance traveled by the laser pointer by the distance to the water's surface. The resulting value is then used in Snell's law to find theta 2.

Q: What is the final calculated distance for the laser pointer?

The final distance is calculated by adding the distance along the surface of the water (x), the incremental distance (y), and the depth of the pool (3 meters). The result is approximately 11.18 meters.

Summary & Key Takeaways

• The video demonstrates a more complex example of using Snell's law to calculate the distance a laser pointer travels in water.

• The process involves determining the distance along the surface of the water and the incremental distance from the surface to the bottom of the pool.

• Trigonometry is used to calculate the angles involved, allowing for the final distance to be calculated.