Reflection and Refraction of Light Chapter 22 Reflection and Refraction of Light Conceptual questions: 9,11,16,17,18 Quick quizzes: 2,3,4 Problems: 21,28,49,56

Dual Nature of Light Experiments display either the wave nature or the particle nature of light Nature prevents testing both qualities at the same time “Particles” of light are called photons Each photon has a particular energy E = h ƒ h is Planck’s constant h = 6.63 x 10-34 J s

Geometric Optics – Using a Ray Approximation Light travels in a straight-line path in a homogeneous medium The ray approximation is used to represent beams of light A ray of light is an imaginary line drawn along the direction of travel of the light beams

Ray Approximation A wave front is a surface passing through points of a wave that have the same phase and amplitude The rays, corresponding to the direction of the wave motion, are perpendicular to the wave fronts

Reflection of Light A ray of light, the incident ray, travels in a medium When it encounters a boundary with a second medium, part of the incident ray is reflected back into the first medium This means it is directed backward into the first medium

Specular Reflection Specular reflection is reflection from a smooth surface The reflected rays are parallel to each other

Diffuse Reflection Diffuse reflection is reflection from a rough surface The reflected rays travel in a variety of directions Diffuse reflection makes the road easy to see at night

Law of Reflection The normal is a line perpendicular to the surface The incident ray makes an angle of θ1 with the normal The reflected ray makes an angle of θ1’ with the normal The angle of reflection is equal to the angle of incidence θ1= θ1’

Reflection of light, quiz

Refraction of Light The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane The angle of refraction, θ2, depends on the properties of the medium v – speed of light

QUICK QUIZ 22.2 If beam 1 is the incoming beam in the figure below, which of the other four beams are reflected and which are refracted?

Refraction Details v1>v2 The angle of refraction is less than the angle of incidence The ray bends toward the normal

Refraction Details v1<v2 The angle of refraction is greater than the angle of incidence The ray bends away from the normal

The Index of Refraction Refraction occurs because the speed of light is different in the two media The index of refraction, n, of a medium can be defined

Frequency Between Media As light travels from one medium to another, its frequency does not change Both the wave speed and the wavelength do change

Index of Refraction Extended f = f1 = f2 v1 = ƒ λ1 v2 = ƒ λ2 The ratio of the indices of refraction of the two media can be expressed as

Snell’s Law of Refraction n1 sin θ1 = n2 sin θ2 θ1 is the angle of incidence 30.0° in this diagram θ2 is the angle of refraction

Table 22.1

Snell’s law, illustration

QUICK QUIZ 22.3 A material has an index of refraction that increases continuously from top to bottom. Of the three paths shown in the figure below, which path will a light ray follow as it passes through the material?

QUICK QUIZ 22.4 As light travels from vacuum (n = 1) to a medium such as glass (n > 1), which of the following properties remains the same: (a) wavelength, (b) wave speed, or (c) frequency?

Problem 22.21 The light shown in the figure makes an angle of 20o with the normal NN’ in the linseed oil (n=1.48). Determine angles q and q’.

Problem 22.28 A cylindrical cistern, constructed below ground level, is 3.0 m in diameter and 2.0 m deep and is filled to the brim with a liquid whose index of refraction is 1.5. A small object rests on the bottom of the cistern at its center. How far from the edge of the cistern can a girl whose eyes are 1.2 m from the ground stand and still see the object?

Dispersion The dependence of the index of refraction on λ is called dispersion

Refraction in a Prism δ the angle of deviation n(l) Since all the colors have different angles of deviation, they will spread out into a spectrum Violet deviates the most Red deviates the least

Using Spectra to Identify Gases All hot, low pressure gases emit their own characteristic spectra The particular wavelengths emitted by a gas serve as “fingerprints” of that gas Some uses of spectral analysis Identification of molecules Identification of elements in distant stars Identification of minerals

The Rainbow At the back surface the light is reflected It is refracted again as it returns to the front surface and moves into the air The rays leave the drop at various angles The angle between the white light and the violet ray is 40° The angle between the white light and the red ray is 42°

Observing the Rainbow

Double rainbow

Huygen’s Principle Huygen assumed that light is a form of wave motion rather than a stream of particles All points on a wave front produce spherical secondary waves, which propagate in the forward direction with speeds characteristic of waves in that medium

Huygen’s Principle and the Law of Refraction In time Δt, ray 1 moves from A to B and ray 2 moves from A’ to C From triangles AA’C and ACB, all the ratios in the Law of Refraction can be found n1 sin θ1 = n2 sin θ2

Total Internal Reflection Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction Ray 5 shows internal reflection

Critical Angle The critical angle is an angle of incidence that will result in an angle of refraction of 90°

Fiber Optics

Conceptual questions 18. If a beam of light with a given cross-section enter a new medium, the cross section of the refracted beam is a) larger b) smaller c) not changed 9. In dispersive materials, the angle of refraction for a light ray depends on the wavelength of light. Does the angle of reflection depend on the wavelength? 11. Explain why a diamond loses most of its sparkle when submerged in carbon disulfide. 16. Explain why an oar partially in water appears to be bent. 17. Why do astronomers looking at distant galaxies talk about looking backward in time?

Problem 22.56 A laser beam strikes one end of a slab of material, as in Figure P22.56. The index of refraction of the slab is 1.48. Determine the number of internal reflections of the beam before it emerges from the opposite end of the slab.

Solution

Problem 21-49 As shown in Figure P22.49, a light ray is incident normally on one face of a 30°-60°-90° block of dense flint glass (a prism) that is immersed in water. (a) Determine the exit angle θ4 of the ray. (b) A substance is dissolved in the water to increase the index of refraction. At what value of n2 does total internal reflection cease at point P?

Review questions 1. Visible light of which color bends the most when changing mediums? A. yellow B. green C. violet D. red

2. Water has an index of refraction of 1. 3 2. Water has an index of refraction of 1.3. Approximately how fast does light move through the water? 1.0 x 108 m/s b. 2.3 x 108 m/s 3.0 x 108 m/s d. 4.9 x 108 m/s 3. The sky is blue because it Absorbs light at 390 nm Reflects light at 390 nm Absorbs light at 700 nm Reflects light at 700 nm