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Chapter 35

The Nature of Light and the Laws of Geometric Optics

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Outline The ray approximation in

geometric optics Reflection

The law of reflection An application: Retroreflection

Refraction Index of refraction Snell’s law of refraction

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The ray approximation in geometric optics

Geometric optics: The study of the propagation of light.

Ray approximation: In the ray approximation, we assume that a wave moving through a medium travels in a straight line in the direction of its rays.

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Reflection Reflection: When a light ray

traveling in one medium encounters a boundary with another medium, part of the incident light is reflected.

Specular reflection: Reflection of light from a smooth surface, where the reflected rays are all parallel to each other.

Diffuse reflection: Reflection from any rough surface, where the reflected rays travel in random directions.

In this book, we use the term reflection to mean specular reflection.

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The Law of reflection Law of reflection: The

angle of reflection equals the angle of incidence: 1

’ = 1. Some definitions:

Normal: The normal is a line drawn perpendicular to the surface at the point where the incident ray strikes.

Angle of reflection and incidence: Measured from the normal to the reflected and incident rays, respectively.

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Example 35.2: The double-reflected light ray

Two mirrors make an angle of 120° with each other. A ray is incident on mirror M1 at an angle of 65° to the normal. Find the direction of the ray after it is reflected from mirror M2.

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Practical applications of reflection Retroreflection: If the angle

between the two mirrors is 90°, the reflected beam will return to the source parallel to its original path.

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Refraction Refraction: When a ray of light

traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray enters the second medium. The part that enters the second medium is bent at the boundary and is said to be refracted.

sin2 / sin1 = v2 / v1 1 and 2 are the angle of incidence and

angle of refraction, respectively. v1 and v2 are the speed of the light in the

first and second medium, respectively. The path of a light ray through a

refracting surface is reversible.

All rays and the normal lie in the same plane.

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Index of Refraction and Snell’s Law of Refraction

Index of refraction n of a medium: n c/v

c = 3 x 108 m/s: speed of light in vacuum. v: speed of light in the medium; v < c. n > 1 for any medium and n = 1 for

vacuum (or approximately in air). Check Table 35.1 for different n values

Snell’s law of refraction: n1sin1=n2sin2

As light travels from one medium to another, its frequency does not change but its wavelength does.

1n1 = 2n2, or 1/2 = v1/v2.

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Examples Problem #21: When the light illustrated

in the figure passes through the glass block, it is shifted laterally by the distance d. Taking n = 1.50, find the value of d.

Example 35.5: A laser in a compact disc player generates light that has a wavelength of 780 nm in air.

(A) Find the speed of light once it enters the plastic of a compact disc (n = 1.55).

(B) What is the wavelength of this light in the plastic?

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Quick Quiz If beam 1 is the

incoming beam in the figure on the left, which of the other four red lines are reflected beams and which are refracted beams?

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Homework

Ch 35, P. 1118, Problems: #6, 12, 22.