Textbook Question
A light ray in air is incident on a transparent material whose index of refraction is n. Find an expression for the (non-zero) angle of incidence whose angle of refraction is half the angle of incidence.
13
views
33. Geometric Optics
Refraction of Light & Snell's Law
7:46 minutesProblem 55
Textbook Question
A horizontal laser beam enters the glass prism shown in FIGURE P34.55. When the laser beam exits the prism, by what angle will it have been deflected from horizontal?
Verified step by step guidance1
Identify the key concepts involved: refraction of light and Snell's Law. Refraction occurs when light passes from one medium to another, changing its speed and direction. Snell's Law is given by: , where is the refractive index and is the angle of incidence or refraction.
Determine the refractive indices of the two media involved. For example, the refractive index of air is approximately , and the refractive index of the glass prism will be given or assumed (e.g., ).
Apply Snell's Law at the point where the laser beam enters the prism. Use the given angle of incidence (or assume it if not provided) to calculate the angle of refraction inside the prism. Rearrange Snell's Law to solve for the angle of refraction: .
Trace the path of the laser beam through the prism. At the second interface (where the beam exits the prism), apply Snell's Law again to calculate the angle of refraction as the beam exits back into the air. Use the angle of incidence at this interface and the refractive indices of the glass and air.
Calculate the total deflection angle. The deflection angle is the difference between the initial direction of the laser beam (horizontal) and its final direction after exiting the prism. Use geometry to determine this angle based on the angles of refraction and the geometry of the prism.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
7mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Refraction
Refraction is the bending of light as it passes from one medium to another, caused by a change in its speed. When light enters a denser medium, like glass from air, it slows down and bends towards the normal line. Conversely, when it exits back into a less dense medium, it speeds up and bends away from the normal. This principle is crucial for understanding how the laser beam behaves as it travels through the prism.
Recommended video:
Guided course
03:46
Index of Refraction
Snell's Law
Snell's Law quantitatively describes the relationship between the angles of incidence and refraction when light passes between two media with different refractive indices. It is expressed as n1 * sin(θ1) = n2 * sin(θ2), where n is the refractive index and θ is the angle relative to the normal. This law is essential for calculating the angles at which the laser beam enters and exits the prism, allowing us to determine the total deflection.
Recommended video:
Guided course
07:59Snell's Law
Total Internal Reflection
Total internal reflection occurs when a light ray attempts to move from a denser medium to a less dense medium at an angle greater than the critical angle, resulting in the light being completely reflected back into the denser medium. While this phenomenon is not directly applicable to the exit of the laser beam from the prism, understanding it helps clarify the behavior of light at the boundaries of different media, which is important for analyzing the overall path of the beam.
Recommended video:
Guided course
05:29Total Internal Reflection
Related Videos
Related Practice