Total internal reflection | Geometric optics | Physics | Khan Academy

Summary

This educational video script delves into the phenomenon of light refraction and total internal reflection. It uses the analogy of a car transitioning from mud to a road to explain how light changes direction when moving from a slow to a fast medium. The script introduces the concept of the critical angle, where light at this angle or greater will reflect back into the medium rather than refract, a principle crucial to understanding fiber-optic cable operation. The example of light exiting water into air, with a critical angle of 48.8 degrees, illustrates Snell's Law and the calculation of this angle.

Takeaways

• 🌟 Light exits a slow medium at an angle, similar to a car moving from mud to road.
• 🚗 The direction of light changes when it moves from a slow to a fast medium, causing the refraction angle to be greater than the incident angle.
• 🔍 There exists a critical angle (theta 3) where the refracted angle is exactly 90 degrees, preventing light from escaping into the fast medium.
• 🌈 Beyond the critical angle, light undergoes total internal reflection, staying within the slow medium.
• 💧 The critical angle can be calculated using Snell's Law, which relates the indices of refraction of the two media involved.
• 📚 Snell's Law formula: ( n_1 σin(θ_1) = n_2 σin(θ_2) ), where ( n_1 ) and ( n_2 ) are the indices of refraction of the slow and fast media, respectively.
• 📉 For the critical angle, the refraction angle is 90 degrees, making ( σin(θ_{critical}) = θ_{critical} = rac{1}{n_1} ).
• 📏 Example calculation: For water (index 1.33) and air (index 1.00), the critical angle is approximately 48.8 degrees.
• 🌐 At the critical angle, light travels along the surface of the medium, not escaping into the air.
• 🌐 Fiber-optic cables utilize total internal reflection to transmit light signals, keeping them confined within the glass.

Q & A

What is the phenomenon described when light exits from a slow medium to a fast medium?

The phenomenon described is refraction, where the direction of light changes as it moves from a slower medium to a faster one, causing the angle of refraction to be larger than the incident angle.

What analogy is used in the script to explain the change in direction of light when moving from a slow to a fast medium?

The script uses the analogy of a car moving from mud (slow medium) to a road (fast medium), where the left tires get out of the mud before the right tires, causing the car to veer to the right.

What is the term for the angle at which the refracted angle becomes 90 degrees, and the light does not escape into the fast medium?

This angle is called the critical angle, and at this point, the light undergoes total internal reflection instead of refracting out of the slow medium.

What is total internal reflection, and how does it occur?

Total internal reflection is a phenomenon where light is completely reflected back into the medium it is traveling through, rather than refracting into another medium. It occurs when the incident angle is larger than the critical angle.

What is Snell's Law, and how is it used to find the critical angle?

Snell's Law relates the angles of incidence and refraction to the indices of refraction of the two media. It is used to find the critical angle by setting the refraction angle to 90 degrees and solving for the incident angle at which this occurs.

What is the index of refraction, and how does it relate to the speed of light in different media?

The index of refraction is a measure of how much light slows down in a medium compared to a vacuum. A higher index of refraction indicates that light travels slower in that medium.

What is the critical angle for light traveling from water to air, given the indices of refraction for water and air?

Given that the index of refraction for water is 1.33 and for air is approximately 1.00, the critical angle can be found using Snell's Law and is approximately 48.8 degrees.

How does the sine function play a role in calculating the critical angle using Snell's Law?

The sine function is used to relate the incident angle to the refraction angle in Snell's Law. Since the refraction angle at the critical angle is 90 degrees, the sine of 90 degrees is 1, simplifying the calculation.

What is the practical application of total internal reflection as described in the script?

Total internal reflection is used in fiber-optic cables to transmit light signals over long distances with minimal loss. The light is kept within the cable through internal reflections.

Why does the refraction angle always increase when light moves from a slower to a faster medium?

The refraction angle increases due to the change in the speed of light as it enters a less dense medium, causing the light to bend away from the normal line at a greater angle.

What is the significance of the unit circle in determining the sine of 90 degrees in the context of Snell's Law?

The unit circle is used to visualize and understand the sine of 90 degrees, which is 1. This is because at 90 degrees, the y-coordinate on the unit circle represents the sine value, which is the height of the point on the circle.