Refraction & Lenses

Refraction of Light

When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray is reflected and part of the ray enters the second medium

The ray that enters the second medium is bent at the boundary

This bending of the ray is called refraction

Refraction of Light, cont

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

Following the Reflected and Refracted Rays

Ray is the incident ray

Ray is the reflected ray

Ray is refracted into the lucite

Ray is internally reflected in the lucite

Ray is refracted as it enters the air from the lucite

More About Refraction

The angle of refraction depends upon the material and the angle of incidence

The path of the light through the refracting surface is reversible

1 2

2 1

sinconstant

sin

v

v

Refraction Details, 1

Light may refract into a material where its speed is lower

The angle of refraction is less than the angle of incidence The ray bends

toward the normal

Refraction Details, 2

Light may refract into a material where its speed is higher

The angle of refraction is greater than the angle of incidence

The ray bends away from the normal

The Index of Refraction

When light passes from one medium to another, it is refracted because the speed of light is different in the two media

The index of refraction, n, of a medium can be defined

speed of light in a vacuum cn

speed of light in a medium v

Index of Refraction, cont

For a vacuum, n = 1

For other media, n > 1

n is a unitless ratio

Some Indices of Refraction

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

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

A ray of light strikes a drop of water in the atmosphere

It undergoes both reflection and refraction

First refraction at the front of the drop

Violet light will deviate the most

Red light will deviate the least

The Rainbow, 2

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

If a raindrop high in the sky is observed, the red ray is seen

A drop lower in the sky would direct violet light to the observer

The other colors of the spectra lie in between the red and the violet

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

A particular angle of incidence will result in an angle of refraction of 90°

This angle of incidence is called the critical angle

21 2

1

sin C

nfor n n

n

Critical Angle, cont

For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary

This ray obeys the Law of Reflection at the boundary

Total internal reflection occurs only when light attempts to move from a medium of higher index of refraction to a medium of lower index of refraction

Fiber Optics

An application of internal reflection

Plastic or glass rods are used to “pipe” light from one place to another

Applications include medical use of fiber

optic cables for diagnosis and correction of medical problems

Telecommunications

Thin Lenses

A thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a plane

Lenses are commonly used to form images by refraction in optical instruments

Thin Lens Shapes

These are examples of converging lenses

They have positive focal lengths

They are thickest in the middle

More Thin Lens Shapes

These are examples of diverging lenses

They have negative focal lengths

They are thickest at the edges

Focal Length of Lenses

The focal length, ƒ, is the image distance that corresponds to an infinite object distance This is the same as for mirrors

A thin lens has two focal points, corresponding to parallel rays from the left and from the right A thin lens is one in which the distance

between the surface of the lens and the center of the lens is negligible

Focal Length of a Converging Lens

The parallel rays pass through the lens and converge at the focal point

The parallel rays can come from the left or right of the lens

Focal Length of a Diverging Lens

The parallel rays diverge after passing through the diverging lens

The focal point is the point where the rays appear to have originated

Lens Equations

The geometric derivation of the equations is very similar to that of mirrors

𝑀 =ℎ𝑖

ℎ𝑜= −

𝑑𝑖

𝑑𝑜

1

𝑓=

1

𝑑𝑜+

1

𝑑𝑖

𝑑𝑜 𝑑𝑖

Lens Equations

The equations can be used for both converging and diverging lenses

A converging lens has a positive focal length

A diverging lens has a negative focal length

Sign Conventions for Thin Lenses

Quantity SymbolInFront

InBack

Convergent Divergent

Object Distance

do + -

Image Distance

di - +

Focal Length

f + -

Lens Radii R1, R2 - +

Focal Length for a Lens

The focal length of a lens is related to the curvature of its front and back surfaces and the index of refraction of the material

This is called the lens maker’s equation

1 2

1 1 1( 1)n

f R R

Ray Diagrams for Thin Lenses

Ray diagrams are essential for understanding the overall image formation

Three rays are drawn The first ray is drawn parallel to the first

principle axis and then passes through (or appears to come from) one of the focal lengths

The second ray is drawn through the center of the lens and continues in a straight line

The third ray is drawn from the other focal point and emerges from the lens parallel to the principle axis

There are an infinite number of rays, these are convenient

Ray Diagram for Converging Lens, do > f

The image is real

The image is inverted

Ray Diagram for Converging Lens, do < f

The image is virtual

The image is upright

Ray Diagram for Diverging Lens

The image is virtual

The image is upright

Spherical Aberration

Results from the focal points of light rays far from the principle axis are different from the focal points of rays passing near the axis

For a mirror, parabolic shapes can be used to correct for spherical aberration

Chromatic Aberration

Different wavelengths of light refracted by a lens focus at different points Violet rays are refracted

more than red rays

The focal length for red light is greater than the focal length for violet light

Chromatic aberration can be minimized by the use of a combination of converging and diverging lenses

C’est Fini