M5 1stSem Final Geometric Optics (Refraction and Lenses)

Objectives:​

• Recognize situations in which refraction will occur.

• Identify which direction light will bend when it passes from one medium to another.

What happens when light hits an object?

• Reflection

• Refraction

• Absorption

Reflection

• Occurs when light bounces off of an object

• Specular & Diffuse Reflections

• The colors we perceive are those that are reflected off of an object.

Refraction

• the bending of light as it changes speed

• some mediums cause light to bend more than others

• index of refraction: a measure of how much a light ray bends when it enters a specific medium

Refraction occurs when light’s velocity changes.
Light passes through transparent materials like glass, water, ice, diamonds, and quartz at different speeds. When light moves from a faster medium (like air) to a slower one (like glass), it bends toward the normal. Conversely, when moving from a slower to a faster medium, it bends away from the normal. If light is parallel to the normal, no bending occurs. The path of light is reversible, meaning it would follow the same path in reverse if the direction were switched.

Refraction can be explained in terms of the wave model of light.
Light waves can be approximated using wave fronts and light rays. When light passes from one medium to another, such as from air to glass, the wave fronts slow down in the new medium. This causes the direction of the wave to change, leading to a shorter wavelength in the glass compared to the wavelength in air. However, the frequency of the light remains unchanged.

Index of Refraction
-the ratio of the speed of light in a vacuum to the speed of light in a given transparent medium

The index of refraction is a dimensionless number always greater than 1, indicating how much slower light travels in a substance compared to a vacuum. A higher index means slower light speed and more bending of light. For example, when light moves from air (low index) to water (high index), it bends toward the normal. When it moves from water to air, it bends away from the normal.

Index of Refraction

Wavelength affects the index of refraction.
The indices of refraction listed are specific to light with a 589 nm wavelength in a vacuum. The bending of light when it enters a different medium depends on both its wavelength and speed. Since each color of light has a different wavelength, each is refracted differently, which is why a prism separates white light into a spectrum of colors.

​Thin Lenses

Objectives:

• Use ray diagrams to find the position of an image produced by a converging or diverging lens, and identify the image as real or virtual.

• Solve problems using the thin-lens equation.

• Calculate the magnification of lenses.

• Describe the positioning of lenses in compound microscopes and refracting telescopes.

​Curved surfaces change the direction of light.
Lenses are used in optical devices like cameras, telescopes, and microscopes to form images. The human eye also uses a lens to focus light on the retina. A typical lens is made of glass or plastic with surfaces shaped as segments of spheres or planes.

Focal length is the image distance for an infinite object distance. The focal point of a lens is where parallel light rays from a distant object converge or appear to originate. A converging lens bends rays inward to meet at the focal point, while a diverging lens spreads rays outward, making them seem to originate from a focal point. Lenses have two focal points, one on each side, and the focal length is the distance from the lens's center to its focal point.

Ray diagrams of thin-lens systems help identify image height and location.
Ray diagrams, similar to those used for mirrors, can be used to predict images formed by lenses. For thin lenses, where the thickness is small relative to the lens's curvature or object distance, we represent the lens as a line segment through its center.

Convex Lens

• Thicker in the center than the edges

• As parallel light rays enter the lens they exit at an angle so they meet at a focal point

• If the object is between the focal point and the lens then a virtual image is produced

• If the object is beyond the focal point then a real image is produced.

Converging lenses (Convex) can produce real or virtual images of real objects.

Concave Lens

• "caves in" on either side of lens

• thinner in the middle than at the edges

• The parallel light rays enter and then exit angled away from one another never meeting at a focal point

• Like a Convex Mirror it produces only virtual images

Diverging lenses (Concave) produces virtual images of real objects.
A diverging lens creates a virtual, upright, and reduced image of a real object placed anywhere relative to the lens. This image always appears inside the focal point.

The Thin-Lens Equation and Magnification

​Ray diagrams provide a visual estimate of image size and distance, but the thin-lens equation can be used to calculate these values more precisely. A real image has a positive image distance, and a virtual image has a negative distance. Converging lenses (Convex) have a positive focal length (positive lenses), and diverging lenses (Concave) have a negative focal length (negative lenses).

Magnification by a lens depends on object and image distances.

Magnification (M) is the ratio of image height to object height and applies to both converging and diverging lenses. The magnification value indicates the image's size and orientation: if the magnitude is less than one, the image is smaller; if greater than one, the image is larger. A negative magnification means the image is real and inverted, while a positive magnification indicates an upright and virtual image.

An object is placed 30.0 cm in front of a converging lens and then 12.5 cm in front of a diverging lens. Both lenses have a focal length of 10.0 cm. For both cases, find the image distance and the magnification. Describe the images.

Dispersion leads to optical phenomena such as rainbows

• ​Caused by reflection, refraction, and dispersion of light in water droplets.

• Always appear opposite the Sun Colors: red, orange, yellow, green, blue, indigo, violet (same as visible light spectrum)

• Usually seen during or after rainfall when sunlight shines through water droplets

​Rainbow

• Best observed when Sun is behind the observer at a low angle Seen in the west during morning, east in evening

• Not visible at noon (Sun overhead)

​Process
1. Sunlight refracts when entering water droplets → scatters into colors
2. Colors reflect inside the droplet
3. Light refracts again when leaving → spectrum forms

• ​One reflection, two refractions

• Colors: red outside, violet inside

• Seen at 40–42° elevation

• Mirage Optical phenomenon caused by refraction of light Produces a displaced image of distant objects.

• Light travels at different speeds in hot air vs. cold air

• Occurs when ground is very hot and air above is cooler

• Hot ground heats the air layer above it → creates temperature gradient

​Mirage

• Appearance of water puddles on roads on hot days due to refraction

​Process
1.Sunlight passes through cooler air into hotter air layer
2.Light bends (refracts) due to speed change
3.Creates an image that can be inverted or upright

​Types of mirrors and their Applications

Hyperopia (farsightedness) occurs when the eye is too short or close objects look blurred, causing their image to form behind the retina.
Convex eyeglasses correct farsightedness by converging light rays so that they meet at the retina.

​Myopia (nearsightedness) happens when the eye is too long or close objects look clear, causing their image to form in front of the retina.
Concave eyeglasses correct nearsightedness by diverging light rays so that they can meet at the retina.

• Color blindness is the inability to distinguish certain colors.

• The cones in the retina of the part of our eye is affected in color blindness.

• A person with red-green color blindness cannot distinguish red and green colors.

• Color blindness is more common in men than in women.

• Device or test used to detect color blindness is the Ishihara color test.

​Color blindness

Multiple Choice

What are three things that can happen when light hits an object?

• Regular, Diffuse, Obtuse

• Reflection, Refraction, and Absorption

• Concave, Convex, Plane

Multiple Choice

Which type of lens is thicker in the middle?

• Concave

• Convex

Multiple Choice

Which describes a convex lens?

• triangular in shape
• more transparent in the middle
• thicker on the edges than in the middle
• thicker in the middle than on the edges

Multiple Choice

When an object is placed between the focal point and the convex lens, the image produced is ___.

• real, reduced, and inverted
• real, enlarged, and inverted
• virtual, enlarged, and upright
• virtual, reduced, and upright

Multiple Choice

Which figure represents the path light takes through a converging lens?

Multiple Choice

An object of height 4 cm is placed 10 cm away from a concave lens of focal length 6 cm as shown below.Image is 

• virtual.inverted,smaller

• virtual,upright,smaller

• real,inverted,bigger

• real,upright, bigger

Multiple Choice

Which lens represents the path light takes through a diverging lens?

Multiple Choice

Which part of your eye would you consider to be the "great messanger"?

• retina
• optic nerve
• sclera
• blood vessels

Multiple Select

Which controls the amount of light entering the eyes. It also give the eye its color?

• lens

• retina

• Iris

• cornea

Multiple Choice

What do you call the cells in the retina that respond to small amounts of lights?

• rods

• cones

Multiple Select

The back part of the eyes that receives an upside down image

• lens

• retina

• brain

• pupil

Multiple Select

What part of the eye is pointed at number 4?

• Iris

• retina

• pupil

• lens

Multiple Select

Which focuses and defocuses light entering the eyes?

• cornea

• Iris

• pupil

• lens

Multiple Choice

It lets light enter the eye

• iris

• retina

• pupil

Multiple Choice

A thin membrane protecting the inner part of the eyes from the outside materials is called ...

• cornea

• retina

• iris

• lens

• pupil

Multiple Choice

What do you call the color part of the eye?

• retina

• optic nerve

• iris

• pupil

Multiple Choice

Which word best describes what happens to light when it "refracts"?

• stops

• bends

Multiple Choice

We do not see the colors that are absorbed, only those that are reflected off of an object.

• True

• False

Multiple Select

What do we call the scale used to identify how much light slows down and bends when entering different materials?

• Index of Refraction

• Scale of Bending

Multiple Choice

Which type of lens in thinner in the middle and thicker on the edges

• Concave

• Convex

Multiple Choice

What type of lens do we have in our eye?

• Concave

• Convex

Multiple Choice

What do we call the back of the eye where images are projected as light?

• pupil

• retina

• iris

• cornea

Multiple Choice

What is the part of the eye that bends light so that an image can be projected onto the retina?

• optic nerve

• lens

• pupil

Multiple Choice

What do we call the muscle in the eye that contracts in sunlight?

• retina

• lens

• pupil

Multiple Choice

What is the protective layer on the outer eye called?

• Cornea

• lens

• pupil