9. Light and Optics

Light

Electromagnetic transverse wave with amplitude perpendicular to each other and to direction of propagation

Polarized Light

Electric and magnetic fields of light point any direction perpendicular to velocity and to each other

Circular Polarization

Electric and magnetic fields slowly rotate over time clockwise or CCW

Speed of Light (c)

3 × 10⁸ m/s

E =

hf = hc/λ

Planck’s Constant (h) =

6.63 × 10^-34

v =

λf

Spectrometers

Measures how matter interacts with EM radiation using light absorbances

How is color perceived?

Apparent color is a result of wavelengths of light NOT absorbed, instead reflecting

Reflection

Wave bounces off new medium

Refraction

Wave continues into new medium, along a different path

Normal Line

Line to which all angles are defined; perpendicular to optical interface

Refractive Index (n) =

c/v (always above 1)

Snell’s Law

n₁sinθ₁ = n₂sinθ₂

Higher the refractive index…

Slower the light moves through medium

Critical Angle

Point where the angle of refracted ray = 90

Total internal Reflection

Beyond critical angle, light can no longer refract and is instead reflected within medium

Dispersion

Breaking up of light due to speed of light varying based on wavelength

Which light bends most?

Violet because it has the shortest wavelength (due to being slowed down most) in dispersive material

Apertures

Barrier with an opening that a wave hits, some is reflected back but some goes through opening and is diffracted

Diffraction

Expansion of light waves outward through a slit

The larger aperture…

the less noticeable diffraction is (wavelengths appear undisturbed)

Unique Property of Light

Acts as both a wave and particle

Pattern of Diffraction

As light hits interface through slit, constructive and destructive interference occurs:

• Constructive creates intensity peaks, areas of light

• Destructive creates dark areas

Single slit formula:

Asinθ = mλ

(minima = dark spots)

Double-Slit Diffraction

Two openings, characterizes by more evenly spread minima and maxima

Double Slit Maxima Formula

Dsinθ = nλ

Double Slit Minima Formula

Dsinθ = (n + ½)λ

Mirrors

Substances from which light only reflects off, without absorbance or refraction

Types of Mirrors

1. Plane

2. Concave

3. Convex

Real vs. Virtual Image

Real images are created when light waves converge, virtual images when light waves diverge but we perceive them as converging

Plane Mirror

Light that hits this mirror bounces back in same direction, reflecting at the same angle but reflected (opposite normal)

Concave Mirrors

Mirrors with an inward curve (converging mirror)

Convex Mirror

Mirrors with an outward curve (diverging mirrors)

Which mirrors form virtual images?

Plane and convex mirrors since the rays of light NEVER converge

Which mirror generates real images?

Concave mirrors because light waves converge

Virtual image by plane mirrors

On the other side of the plane, same size, and same orientation

Focal Point

Point at which incident rays converge

Where is the focal point of concave mirror located?

On the same side of the object

Where is the focal point located in convex mirror?

On the opposite side of the image (behind lens)

Distance of object (o)

Location of object relative to mirror

Distance of image (i)

Where the image of the object is formed

Thin Lens Equation

1/f = 1/o + 1/i

-f value means…

The image is virtual

Sign conventions for mirrors:

In front of mirror is positive, behind is negative

• Concave f > 0

• Convex f <0

Magnification (m) =

-i/o

A negative magnification means…

The image is inverted and REAL

Drawing Ray Diagrams

1. Draw one ray parallel to normal from object, reflecting through focal point

2. Second ray extending from object through focal point, reflecting and traveling parallel to normal

3. Image is where the two rays intersect

Magnification for convex mirrors

Positive, meaning image will be upright

For mirrors, the sign of o is always:

Positive, because objects are in FRONT of mirrors

If o>f,

The image is real and inverted (because magnification is negative); concave mirror

If o<f,

The image is virtual because i will be negative, and magnification will be positive (upright is virtual)

Lenses

Materials through which light is reflected both upon and entering and exiting

Convex (converging) lenses are similar to …

Concave mirrors

Concave (diverging) lenses are similar to…

Convex mirrors

When should you use lens-makers formula?

When you have to account for the thickness of the lens

Lens-Makers Formula

1/f = (n-1)(1/r₁ - 1/r₂)

Optical Power (OP) =

1/f (diopters, m^-1)

Must be meters

Optical Power

How powerful a lens is, how much it bends light

Negative OP and f correspond to…

Diverging lens

Positive OP and f correspond to…

Converging lens

Spherical Aberration

Difference in the refraction patterns of light rays close to center vs on the edge of a sphere

How to solve multi-lens systems:

1. Find image created by first lens

2. Use created image as object for second lens

Total magnification =

m₁ x m₂

Farsightedness (hyperopia)

Lens doesn’t bend light enough and image is formed behind the retina, so a converging lens is needed to correct

Nearsightedness (myopia)

Lens refracts too much light, making the image in front of retina, so a diverging lens must be used

What lens is used to treated myopia/nearsightedness?

Diverging lens

What lens is used to treat hyperopia/farsightedness?

Converging lens