Light, Reflection, Refraction, Total Internal Reflection, Lenses, Magnifying Glasses and Dispersion

Light: Exploring How Light Travels (Grade 10)

Reflection (Aufaa Nurjihan)

Objectives:
- Define and use the terms: normal, angle of incidence, and angle of reflection.
- Describe the formation of an optical image by a plane mirror and its characteristics (same size, same distance from mirror, virtual).
- Understand that the image in a plane mirror is virtual.
- Define the law of reflection as angle of incidence = angle of reflection and use this relation.
- Perform simple constructions, measurements, and calculations for reflection by plane mirrors.

Looking in the Mirror

Light usually travels in straight lines but changes direction when it hits a shiny surface.
This change in direction at a shiny surface like a mirror is called reflection.
When light rays from an object hit a plane mirror, they reflect off the mirror at the same angle at which they arrive but in a different direction.

The Ray Model of Light

Light travels in straight lines called rays.
Rays have arrows indicating the direction of travel.
Example: a beam of light from a laser.
A ray travels in a straight line until it hits something, like a mirror.

Reflection, Absorption, and Transmission

Reflection: Light bounces off a surface.
Absorption: Materials take in light, often converting it to heat.
Transmission: Light passes through a transparent material, like glass or water.
When light rays encounter an object, they can be reflected, absorbed, or transmitted.

Ray Diagrams

We can represent how light interacts with materials using a ray diagram.
It represents the possible paths light can take from a source or an object to an observer or a screen.

Angle of Incidence and Angle of Reflection

Law of Reflection: The angle of incidence (i) equals the angle of reflection (r).
i = r
Angle of Incidence (i): The angle at which the incoming light ray hits the mirror.
Angle of Reflection (r): The angle at which the light ray leaves the mirror.
Normal: A line perpendicular to the plane mirror.

Learning Check - Angles of Incidence and Reflection

If a light ray hits a plane mirror at an angle of 30° to the surface, the angles of incidence and reflection are both 60°.
i = 90° - 30° = 60°
Since i = r, then the angle of reflection (r) is also 60°.

Mirrors: Drawing a Ray Diagram

Steps for drawing ray diagrams for plane mirrors:
1. Draw an incoming ray (incident ray) from the object to the mirror.
2. Draw the line perpendicular to the plane mirror (normal), then draw the reflected ray, following the law of reflection.
3. Draw another incident ray from the same point on the object, along with its corresponding reflected ray.
4. Extend both reflected rays backwards behind the mirror until they meet, using dashed lines since these are not real rays.
5. The point where the extended rays meet is the location of the image.

Characteristics of an Image Formed by a Plane Mirror

Upright: The image is the same way up as the object.
Same size: The image is the same size as the object.
Laterally inverted: The left side of the object appears as the right side of the image.
Same distance: The image is the same distance behind the mirror as the object is in front.
The image formed by a plane mirror is virtual.

Learning Check - Ray Diagrams

For an eye observing an object P by reflection in a plane mirror, the correct ray diagram accurately shows the reflected rays and their extensions, with the angle of reflection and incidence being approximately equal. The extended reflected rays intersect at a point located the same distance from the mirror as the object.

The Pinhole Camera

A pinhole camera is a simple device that captures images without a lens, operating on the principle of light travelling in straight lines.
Light passing through the tiny pinhole projects an upside-down and smaller image on the screen.
Rays coming from the image intersect at the pinhole and continue to travel in a straight line.

Review

Ray Model of Light: Uses the concept that light travels in straight lines, represented by rays.
Ray Diagram: Represents the possible paths that light can take from the source to the observer or screen.
Images on Plane Mirrors: Plane mirrors create images that are upright, the same size, laterally inverted, and located at the same distance from the mirror as the object.

Refraction (Aufaa Nurjihan)

Objectives:
- Define and use the terms normal, angle of incidence, and angle of refraction.
- Describe the passage of light through transparent material (limited to the boundaries between two media only).
- Describe an experimental demonstration of the refraction of light.
- Define the refractive index, n, in terms of the equation n = c/v; recall and use this equation.
- Define the law of refraction using the equation n = \frac{\sin i}{\sin r}; recall and use this equation.

Refraction

Refraction is the bending of rays of light when they travel from one medium to another.
The straw appears bent due to the refraction of light coming from the part of the straw that is underwater.

Ray Model of Light

Refraction happens at the boundary between two materials.
Incident ray: The ray approaching the boundary.
Refracted ray: The ray leaving the boundary.
The angle of incidence, i, and angle of refraction, r, are measured to the normal drawn at the point where the ray hits the boundary.

Refraction and Density

The change in direction depends on the difference in density between the two media:
- From less dense to more dense (e.g., air to glass), light bends towards the normal.
- From more dense to less dense (e.g., glass to air), light bends away from the normal.
- When passing along the normal (perpendicular), the light does not bend at all.

Refraction Explanation

To explain why a change in speed causes bending, picture a truck's wheels slipping off the road into the sand. The truck turns to the side because it cannot move as quickly through the sand.

Refractive Index

When a ray of light passes from air into glass, it slows down and bends towards the normal.
The refractive index of a material is a measure of how much the light slows or how much it is bent.

Refractive Index Equations

The refractive index, n, for the ratio of speeds is given by the equation: n = c/v (where c is the speed of light in vacuum and v is the speed of light in the medium).
The refractive index, n, for the ratio of angles is given by the equation: n = \frac{\sin i}{\sin r}.

Example - Refractive Index of Water

A ray of light hits the surface of water at an angle of incidence of 30°. It is refracted at an angle of 22°. Find the refractive index, n, of water.

Example - Light Entering a Glass Block

A ray of light enters a glass block of refractive index 1.53, making an angle of 15° with the normal before entering the block. Calculate the angle it makes with the normal after it enters the glass block.

Total Internal Reflection (Aufaa Nurjihan)

Objectives:
- State the meaning of critical angle.
- Describe internal reflection and total internal reflection using both experimental and everyday examples.
- Recall and use n = 1/\sin c.
- Describe and explain the action of optical fibres, particularly in communications technology.

Internal Reflection

When a ray of light strikes a glass block, it enters the block without bending because it is directed along the radius of the block.
When light emerges from the glass, some light is reflected back inside the glass. This is called internal reflection.

The Ray Model of Light and Total Internal Reflection (TIR)

a: Small angle of incidence, most light emerges, faint reflected ray.
b: Increased angle of incidence, more light reflected, refracted ray bends further.
c: Refracted ray emerges parallel to the surface at the critical angle. Most light is reflected.
d: Angle of incidence greater than the critical angle, all light is reflected inside the block (Total Internal Reflection).

Total Internal Reflection (TIR)

Total because 100% of the light is reflected.
Internal because it happens inside the glass.
Reflection because the ray is entirely reflected.

Refractive Index & Critical Angle Equation

\sin c = \frac{1}{n}
The larger the refractive index of a material, the smaller the critical angle.
Light rays inside a material with a high refractive index are more likely to be totally internally reflected.

Example - Critical Angle for Diamond

Find the critical angle, c, for diamond. Assume the refractive index n = 2.40.
- Step 1: Substitute the value of n in the equation: \sin c = \frac{1}{2.40} = 0.417
- Step 2: Rearrange to make c the subject: c = \sin^{-1} 0.417
- Step 3: Answer c = 24.6°

Example - Opals and Diamonds

Compare the critical angles of opal (n \approx 1.5) and diamond (n \approx 2.4) and explain which stone would appear to sparkle more.
Total internal reflection occurs when the angle of incidence of light is larger than the critical angle (i > c).
For opal, total internal reflection occurs for angles of incidence between 42° and 90°.
Since the critical angle of diamond is lower than that of opal, light rays will be totally internally reflected in diamond over a larger range of angles (25° to 90°).
Therefore, diamond will appear to sparkle more than opal.

Lenses (Aufaa Nurjihan)

*Objectives:

Describe the action of thin converging and thin diverging lenses on a beam of light.
Define and use the terms focal length, principal axis, and principal focus (focal point).
Draw and use ray diagrams for the formation of a real image by a single lens.
Describe the characteristics of an image using the terms enlarged / same size / diminished, upright / inverted, and real / virtual.
Know that a virtual image is formed when diverging rays are extrapolated backwards and does not form a visible projection on a screen.

Lenses

Converging lenses are fatter in the middle than at the edges.
Diverging lenses are thinner in the middle than at the edges.

Ray Diagram of Lenses

Principal axis: An imaginary line passing through the center of the lens.
Principal focus (focal point): The point where parallel rays of light converge (converging lens) or appear to diverge from (diverging lens).
Focal length: The distance from the lens to the principal focus.

Converging Lens (Convex Lens)

Parallel rays of light are brought to a focus at the principal focus.
The distance from the lens to the principal focus is the focal length.
The more curved the lens, the shorter the focal length.

Diverging Lens (Concave Lens)

Parallel rays of light are made to diverge (spread out) from a point.
The principal focus is the point from which the rays appear to diverge from.

Worked Example

Drawing a ray diagram to find the image formed of a 3 cm tall object placed 12 cm from a converging lens with a focal length of 5 cm.

Magnifying Glasses (Aufaa Nurjihan)

*Objectives:

Draw and use ray diagrams for the formation of a virtual image by a single lens.
Describe the use of a single lens as a magnifying glass.
Describe the use of converging and diverging lenses to correct long-sightedness and short-sightedness.

Magnifying Glasses

A magnifying glass is a converging lens.
You hold it close to a small object and peer through it to see a magnified image.

Lenses - Image Characteristics

Ray 1 is unrefracted as it passes through the centre of the lens.
Ray 2 starts off parallel to the axis and is refracted by the lens so that it passes through the principal focus.
The image formed is:
- upright
- enlarged
- further from the lens than the object
- virtual

Using Lenses to Correct Eyesight Problems

Parallel light from a distant object is focused by a weak lens.
Diverging light from a close object needs a stronger lens.

Short Sight (Myopia)

A person with short sight can see close-up objects clearly but cannot form a clear image of distant objects.
The image is formed in front of the retina, usually because the eyeball is slightly too long.
To correct this, a diverging lens is used to make the rays from the distant object diverge.

Long Sight (Hyperopia)

A long-sighted person can focus on distant objects but not close objects.
This can be because the eyeball is too short, or the lens cannot become strong enough.
A converging lens causes the rays to converge and corrects this problem.

Dispersion of Light (Aufaa Nurjihan)

*Objectives:

Describe, qualitatively, the dispersion of light as shown by the refraction of light by a glass prism.
Know the traditional seven colors of the visible spectrum in their correct order.
Recall that visible light of a single frequency is described as monochromatic.

Dispersion

When white light passes through glass, it refracts as it enters and leaves the glass and can be split into a spectrum of colours.
This splitting up of white light into a spectrum is known as dispersion.

Monochromatic Light

Light of a single colour is not dispersed by a prism.
It is refracted so that it changes direction but is not split up into a spectrum.
This light is described as monochromatic (mono = one, chromatic = coloured).
Monochromatic light is light of a single frequency.