01:750:109 Lecture Notes - Lecture 10: Seismic Refraction, Curved Mirror, Reflecting Telescope

21 views6 pages

rubyclam909

19 Oct 2018

School

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

Document Summary

Some goes into next boundary - refracted wave. Angle of incidence (angle between incident wave and normal) = angle of reflection (between reflected wave and normal) no matter what. If refracted wave is propagating slower than incident wave, angle of refraction is smaller then angle of incidence. If transmitted wave is propagating slower than incident wave, bent toward normal. Refraction - bending of a wave due to a change in speed of a wave. Reflection - bouncing of a wave off of another medium with no change in angle. Light propagates slower through water, and even slower through glass. Distance of the image behind mirror is same as distance in front of it. Reflected light rays converge at middle point (point = focal point) Distance from mirror to that point = focal length. Glass thicker in middle than at edges (convex lens) Light rays converge a little in glass. After they reach the air - rays converge.

Related Questions

Huygens' principle (first described by the Dutch scientist Christiaan Huygens in 1678) uses geometry to determine the shape of a wavefront at a time t, given some initial wavefront at an earlier time. This can be constructed by imagining that the initial wavefront is a source of wavelets that propagate from each point at the speed of light. From this principle, one can determine the angles of reflection and refraction by considering the speed of light at each point on the wavefront. In this problem, we will explore some of these concepts.

Part A

First, let's look at a plane wave that is incident on a flat piece of material with an index of refraction n. Part of the light is transmitted through the material and part of it is reflected. For the moment, let's just look at the part that is transmitted. At time t=0, the wavefront is a distance d away from the surface of the material. At time t=t₁, the wavefront is at the position of the material interface. Use the Huygens' principle to determine how far into the material (d') the wavefront has propagated by time t=2t₁.

Express your answer in terms of the variables n, t₁, and the speed of light in a vacuum c.

Note that there would be no change in the direction of the wavefront at any point because the wavefront encountered the material interface at the same time at all points. Thus, all of the individual wavefronts all propagated at the same speed, thereby maintaining the flat wavefront.

Now, instead of having a flat wavefront propagating normal to the material interface, we have a flat wavefront propagating toward the material at an angle of 55° to the axis perpendicular to the material interface. In this part, we will look at the relative positions of a few points—A, B, and C—on the wavefront to illustrate Huygens' principle. (Intro 1 figure) Point C touches the vacuum/material interface at time t=0 whereas point B is a distance d and point A is a distance 2d away from the interface.

Part B

What is the time t_B it will take for point B of the wavefront to encounter the vacuum/material interface?

Express your answer numerically to two decimal places in units of t₁ (the time it takes light to travel a distance d in a vacuum).

It should be noted that the accuracy of the method increases the smaller the distance is before making a new wavefront and redoing the wavelets. If you tried to just draw a large wavelet from point B, then it would hit the surface after only traveling a distance d. This large wavelet would make it difficult to visualize how to add up all of the other wavelets to make a coherent wavefront. As a result, one should just draw a line perpendicular to the wavefront at point B until it hits the surface, at which point the wavelets will change owing to the new index of refraction.

Part C

How far did point C go into the material interface in the time t=t_B that it took for point B to get to the interface? For this part we are looking for the distance traversed by the point C in the material (d_C).

Give your answer in terms of the time t_B, c, and n.

Part D

What is the new angle θ at which point C of the wavefront is propagating (relative to a line perpendicular to the vacuum/material interface)? Try to use the fact that you have a spherical wavefront propagating from t=0 at the point where C met the vacuum/material interface until time t_B when the wavefront at point B reached the interface.

Express your answer in terms of inverse trigonometric functions and n.

greenduck607

01:750:109 Lecture Notes - Lecture 10: Seismic Refraction, Curved Mirror, Reflecting Telescope

Document Summary

Get access

Related textbook solutions

Physics: Principles with Applications

Related Documents

RIU 320 Study Guide - Final Guide: Rayleigh Scattering, Specular Reflection, Sound

PHYS 1510 Lecture Notes - Lecture 9: Total Internal Reflection, Rakshasa, Vale Limited

CHEM 101 Lecture Notes - Lecture 17: Total Internal Reflection, Transverse Wave, Circular Polarization

Related Questions