Light and Optics: Waves, Mirrors, Refraction, and Equations

What is a luminous source?

A source that produces its own light.

What is an illuminated source?

An object that is visible because it reflects light from another source.

What is luminous flux?

The total visible light emitted by a source; measured in lumens (lm).

What is illuminance?

The amount of light reaching a surface; measured in lux (lm/m²).

What is luminous intensity?

The light emitted in a particular direction; measured in candela (cd).

What is diffraction?

The bending or spreading of a wave around an obstacle or through an opening.

What are the primary colors of light?

Red, green, and blue.

What are the secondary colors of light?

Cyan, magenta, and yellow.

What is polarized light?

Light whose waves vibrate in one direction.

How do we know light travels through a vacuum?

Sunlight travels through space to Earth; sound cannot travel through a vacuum.

Which visible color has the shortest wavelength?

Violet.

What is the approximate visible-light wavelength range?

About 400 nm to 700 nm.

What colors are in white light?

All colors of visible light.

Why does an object look black?

It absorbs most of the light that hits it and reflects very little.

What happens to wavelength when frequency increases in the same medium?

Wavelength decreases.

What happens to illuminance when distance from a point source doubles?

It becomes one-fourth as great.

Does moving a lamp farther away change its luminous intensity?

No, its luminous intensity stays the same, but illuminance decreases.

Why does red cellophane make white light look red?

It transmits red light and absorbs most other colors.

What happens to blue and green light passing through red cellophane?

Most of it is absorbed.

What is the point-source illuminance equation?

E = I/d², where I is luminous intensity and d is distance.

What is the illuminance equation using luminous flux?

E = Φ/(4πr²), for a source radiating equally in all directions.

What is the inverse-square law for light?

Illuminance is inversely proportional to distance squared: E ∝ 1/d².

What is the wave speed equation?

v = fλ (speed = frequency × wavelength).

What is the speed of light in a vacuum?

Approximately 3.00 × 10⁸ m/s.

What is the speed of light in a medium equation?

v = 1/√(με), or v = c/√(μᵣεᵣ) when relative values are given.

How do you calculate frequency from speed and wavelength?

f = v/λ.

What is a plane mirror?

A flat mirror.

What is a concave mirror?

A mirror that curves inward.

What is a convex mirror?

A mirror that curves outward.

What is the principal axis?

The line through the center of a spherical mirror and its focal point.

What is the normal?

A line perpendicular (90°) to the surface at the point where the ray hits.

What is the focal point (F)?

The point where parallel reflected rays meet or appear to come from.

What is the center of curvature (C)?

The center of the sphere of which the mirror is a part.

What is the relationship between radius/center of curvature and focal length?

R = 2f, so the focal length is half the radius of curvature.

What is a real image?

An image formed where light rays actually meet; it can be projected onto a screen.

What is a virtual image?

An image formed where light rays only appear to meet; it cannot be projected onto a screen.

What is magnification?

The ratio of image size to object size.

What is spherical aberration?

Rays hitting different parts of a spherical mirror do not all focus at the same point.

What is specular reflection?

Reflection from a smooth surface that keeps rays organized and can form a clear image.

What is diffuse reflection?

Reflection from a rough surface that scatters light in many directions.

What is the law of reflection?

The angle of incidence equals the angle of reflection; both angles are measured from the normal.

If a ray makes 47° with the mirror surface, what is its angle from the normal?

90° − 47° = 43°.

What is the image in a plane mirror like?

Upright, virtual, same size as the object, and the same distance behind the mirror as the object is in front.

How do you show that an image is real?

Place a screen (such as paper) where the image forms; a real image can be projected onto it.

Where must an object be for a concave mirror to form a virtual image?

Between the mirror and its focal point.

What kind of image does a convex mirror form?

Always upright, smaller, and virtual for a real object.

What is an advantage of a convex mirror on a vehicle?

It provides a wider field of view.

What is the mirror equation?

1/f = 1/do + 1/di.

What is the magnification equation for mirrors?

m = −di/do = hi/ho.

What does positive image height (hi) mean?

The image is upright.

What does negative image height (hi) mean?

The image is inverted.

What does positive image distance (di) mean for a mirror?

The image is real and in front of the mirror.

What does negative image distance (di) mean for a mirror?

The image is virtual and behind the mirror.

What does positive focal length (f) mean for a mirror?

The mirror is concave.

What does negative focal length (f) mean for a mirror?

The mirror is convex.

What is refraction?

The change in direction of light when its speed changes as it enters another medium.

What is index of refraction?

A measure of how much light slows in a material.

What is the index-of-refraction equation?

n = c/v.

What is Snell's law?

n₁ sin θ₁ = n₂ sin θ₂.

What happens when light goes from air into glass at a nonzero angle?

It bends toward the normal; the incidence angle is larger than the refraction angle.

What happens when light goes from glass into air at a nonzero angle, if it exits?

It bends away from the normal; the refraction angle is larger than the incidence angle.

At what incidence angle does light pass straight through a boundary without bending?

0° (along the normal).

How does light speed change as index of refraction increases?

Light speed decreases.

What is the critical angle?

The incidence angle in the higher-index material that makes the refracted ray travel along the boundary.

What is the critical-angle equation?

θc = sin⁻¹(n₂/n₁), where n₁ > n₂.

What is total internal reflection?

When light is reflected completely back into a higher-index material instead of refracting out.

When can total internal reflection happen?

When light travels from a higher-index medium to a lower-index medium and the incidence angle exceeds the critical angle.

What is dispersion?

The separation of light into different colors because different wavelengths refract by different amounts.

Why does a prism bend violet light more than red light?

Violet light travels more slowly in the prism and is refracted more.

Which pair has the smaller critical angle: air-glass or air-water?

Air-glass: about 44.1°, compared with about 48.8° for air-water.

What is the first principal ray for a concave mirror?

A ray parallel to the principal axis reflects through the focal point.

What is the second principal ray for a concave mirror?

A ray passing through the focal point reflects parallel to the principal axis.

What is the third principal ray for a concave mirror?

A ray passing through the center of curvature reflects back along itself.

How do you draw a ray for a convex mirror that starts parallel to the principal axis?

It reflects outward as if it came from the focal point behind the mirror; extend it backward with a dotted line.

What is the first step when drawing a reflection or refraction diagram?

Draw the surface boundary and the normal perpendicular to it.

How does a ray reflect from a plane mirror?

Draw the reflected ray on the opposite side of the normal at the same angle as the incoming ray.

How does light bend entering a higher-index medium?

Toward the normal.

How does light bend entering a lower-index medium?

Away from the normal, if it refracts out.

What does c mean in light equations?

The speed of light in a vacuum, approximately 3.00 × 10⁸ m/s.

What does v mean in wave/light equations?

The speed of the wave in the medium.

What does f mean in wave equations?

Frequency, measured in hertz (Hz).

What does λ mean?

Wavelength, often measured in meters (m).

What does do mean in the mirror equation?

Object distance.

What does di mean in the mirror equation?

Image distance.

What does ho mean?

Object height.

What does hi mean?

Image height.

How do you find the focal length if the radius of curvature is known?

f = R/2 for a spherical mirror; use a negative sign for a convex mirror under the usual mirror sign convention.

How do you solve equal-illuminance lamp problems?

Set I₁/d₁² = I₂/d₂² and solve for the unknown distance.

How do you solve a round-trip light travel-time problem?

Convert the one-way distance to meters, double it, then divide by 3.00 × 10⁸ m/s.

How do you solve a radar frequency problem?

Convert wavelength to meters, then calculate f = c/λ.

How do you solve a light-speed-in-a-medium problem using relative permeability and permittivity?

Use v = c/√(μᵣεᵣ).

How do you solve for image height?

Find m = −di/do, then use hi = mho.

What should you do with centimeters or nanometers before using SI equations?

Convert to meters when using speed in m/s; 1 cm = 0.01 m and 1 nm = 10⁻⁹ m.