Optics

Electromagnetic wave

Electric and magnetic fields traveling through empty space at the speed of light (c = 3.0 × 10⁸ m/s).

By an accelerating (oscillating) charged particle.

How are electromagnetic waves generated?

A changing electric field produces a magnetic field, and a changing magnetic field produces an electric field.

What is the relationship between electric and magnetic fields in an EM wave?

Electromagnetic Spectrum

The range of energy from low-energy/long-wavelength (radio waves) to high-energy/short-wavelength (gamma rays).

The number of waves to cross a point in 1 second. Unit: Hertz

Define Frequency (f or v) and its unit.

Wavelength

The distance from crest to crest on a wave (measured in meters).

What is the formula for the Speed of Light in relation to waves?

They are inversely proportional (long wavelength = low frequency; short wavelength = high frequency).

What is the relationship between frequency and wavelength?

Ray Model of Light

The assumption that light travels in straight lines, represented by rays emanating from an object.

Index of Refraction (n)

The ratio of the speed of light in a vacuum to the speed of light in a material

Plane of Incidence

The single plane containing the incident ray, reflected ray, refracted ray, and the normal line.

Law of Reflection

The angle of incidence is equal to the angle of reflection.

Law of Refraction (Snell's Law)

The ratio of the sines of the angles is EQUAL to the INVERSE ratio of the indices of refraction)

Critical Angle

The angle of incidence that produces an angle of refraction of 90 DEGREES when light travels from a higher to a lower index of refraction.

Total Internal Reflection

When light travels from a higher n to a lower n, and the angle of incidence is GREATER than the critical angle, resulting in zero transmission (100% reflection).

Mirror

A reflective surface that does not allow light to pass through, but instead bounces it off to produce an image.

Plane Mirror

A flat mirror made by placing a thin layer of silver nitrate or aluminum behind a flat piece of glass.

Diffuse Reflection

Reflection from a rough surface where parallel rays are reflected in many different directions (e.g., distorted water).

Specular Reflection

Reflection from a smooth surface where parallel rays are reflected in the same direction (e.g., plane mirror).

• Image is as far behind the mirror as the object is in front.

• Left-right reversal (lateral inversion).

• Virtual image (light does not flow from it).

What are the properties of an image formed by a plane mirror?

Spherical Mirror

A mirror shaped like a section of a sphere, with the reflective surface on the inside (concave) or outside (convex).

Spherical Aberration

The failure of parallel rays to converge at the same focal point when striking a spherical mirror with large curvature.

Ray Diagram: Parallel Ray

Drawn parallel to the optic axis. Reflects through the focal point (F) for concave, or appears to come from the focal point for convex.

Ray Diagram: Focal Ray

Drawn through (or toward) the focal point (). Reflects parallel to the optic axis.

Ray Diagram: Radial Ray

Drawn through or away from the center of curvature (). Intersects the surface normally and reflects back on itself.

Ray Diagram: Central Ray

Drawn to the vertex V. It is reflected forming equal angles with the optic axis.

Real Image

An image formed when light rays converge at a point. It can be projected onto a screen and is usually inverted.

Virtual Image

An image formed when light rays diverge but appear to meet if extended backward. It cannot be projected on a screen and is always upright/erect.

True. Virtual images are always erect/right-side up.

True or False: All virtual images are upright.

Concave Mirror: Object is between the Surface (Vertex) and the Focal Point ().

• L: Behind the mirror (farther than object)

• O: Upright (Right-side up)

• S: Larger/Magnified

• T: Virtual

Concave Mirror: Object is between Focal Point (F) and Center of Curvature (C).

• L: Beyond

  (Farther from mirror)

• O: Inverted (Upside down)

• S: Larger/Magnified

• T: Real

Concave Mirror: Object is at the Center of Curvature (C)

• L: At C

• O: Inverted

• S: Same size

• T: Real

Concave Mirror: Object is Beyond the Center of Curvature (C)

• L: Between

  and

• O: Inverted

• S: Reduced/Smaller

• T: Real

No image is formed. The reflected/refracted rays are parallel and never intersect (they meet at "infinity").

What happens if an object is placed exactly at the Focal Point () of a concave mirror or convex lens?

Concave mirrors and Convex lenses (depending on how close the object is to the focal point).

Which type of mirror/lens can form both real and virtual images?

• Location: Behind the mirror (closer to mirror than object)

• Orientation: Upright (Right-side up)

• Size: Smaller (Diminished)

• Type: Virtual

Image properties of a Convex Mirror.

Negative (Virtual)

d_i is always positive or negative?

Positive (Upright)

h_i is always positive or negative?

Lens

A transmissive optical device that focuses or disperses light beams using refraction.

Converging (Convex) and Diverging (Concave)

What are the two main types of lenses?

• Location: Can be closer, farther, or same side (depends on object placement).

• Orientation: Inverted or Erect (depends on object placement).

• Size: Smaller, larger, or same (depends on object placement).

• Type: Virtual or Real.

• Note: Properties are similar to a concave mirror.

Properties of a Converging (Convex) Lens.

They converge at the focal point on the opposite side.

What happens to light rays parallel to the principal axis passing through a converging lens?

• Location: Same side as object.

• Orientation: Erect (Upright).

• Size: Smaller (Diminished).

• Type: Virtual.

Properties of a Diverging (Concave) Lens.

They refract and diverge, appearing to originate from the focal point on the same side as the object.

What happens to parallel light rays passing through a diverging lens?

Ray Tracing Rule 1 for Converging Lens

Back: Rays parallel to the principal axis pass through the focal point (F) on the other side.

Ray Tracing Rule 2 for Converging Lens

Rays passing through the focal point (F) emerge parallel to the principal axis.

Ray Tracing Rule 3 for Converging Lens.

Rays passing through the center of the lens pass straight through without deflection.

Ray Tracing Rule 1 for Diverging Lens

Parallel rays are deflected such that when extended backwards, they appear to be coming from the focal point on the same side.

Ray Tracing Rule 2 for Diverging Lens

Similar to a converging lens, central rays (rays passing through the optical center) do not bend.

Ray Tracing Rule 3 for Diverging Lens

Rays heading towards the focal point on the opposite side are deflected to travel parallel to the axis.

Positive (+): Real image (forms on opposite side).

Negative (-): Virtual image (forms on same side).

Image distance (d) sign convention for REAL vs. VIRTUAL images

Negative (-): Inverted image.

Positive (+): Upright image

Image height (h_i) sign convention for INVERTED vs. UPRIGHT images

Virtual, upright, and smaller (diminished)

What type of image does a diverging lens always produce?

The image formed by the first lens becomes the object for the second lens.

Combination of lenses: How is the image of the first lens treated?

Relates the radii of curvature (R1, R2) of the two lens surfaces, and the index of refraction (n) to the focal length (f).

What does the Lensmaker’s equation relate?

Myopia (Nearsightedness)

Issue: Eyeball is too long; image focuses in front of the retina.

Correction: Concave (diverging) lens.

Hyperopia (Farsightedness)

Issue: Eyeball is too short; image focuses behind the retina.

Correction: Convex (converging) lens.