Partial Reflection and Total Internal Reflection

Partial Reflection and Total Internal Reflection

• Key terms:

  • Partial reflection

  • Refraction

  • Critical angle

  • Total internal reflection

Introduction to Partial Reflection and Total Internal Reflection

• When a diver looks up from underwater, they can only clearly see objects in the area directly above them.

• Objects outside this area are not visible because light from these objects does not penetrate the water's surface.

• Light is energy and cannot disappear; it is either reflected or refracted at the boundary between two media (e.g., air and water).

• The amount of reflection and refraction depends on the conditions at the boundary.

Partial Reflection and Refraction

• Partial reflection and refraction: Some light reflects and some light refracts at a surface between two media with different indices of refraction.

• The amount of reflection versus refraction depends on the angle of incidence and the relative indices of refraction.

• When light travels from air into water:

  • At a near-zero angle of incidence (light traveling directly toward the water), most light penetrates and very little is reflected.

  • As the angle of incidence increases, more light is reflected and less is refracted.

• Example: Sunlight on water

  • When the sun is overhead, very little reflection is seen because most of the light penetrates the surface.

  • When the sun is near the horizon, much of the light is reflected, appearing as a blinding reflection.

Definition:

• Partial reflection and refraction: $partial\ reflection\ and\ refraction$ is a phenomenon in which some of the light that is traveling from one medium into another is reflected and some is refracted at the boundary between the media.

Reflection and Refraction in a Rearview Mirror

• Rearview mirrors in cars have a lever to adjust the amount of light reaching the driver's eyes.

  • During the day, drivers need a clear view of traffic.

  • At night, drivers don't want to be blinded by headlights.

Activity 11-2: Investigating Properties of Light

• Materials:

  • Glass block

  • Sheet of paper

  • Ray box (single slit)

  • Pencil

  • Ruler

  • Protractor

• Procedure:

  1. Draw an outline of the glass block on the paper.

  2. Shine a light ray toward the longest side of the block.

  3. Mark the incident, reflected, and emergent rays.

  4. Remove the block and connect the dots to show the path of the light ray.

  5. Draw normals at the points where the incident ray enters and the emergent ray leaves the block.

  6. Measure the angles of incidence $i$, reflection $r$, and refraction $R$, as well as angles $a$ and $b$.

• Observations:

  • Angle of incidence $i$ is equal to the angle of reflection $r$.

  • The refracted ray bends towards the normal when entering the glass and away from the normal when exiting.

How a Rearview Mirror Works

• Rearview mirrors are wedge-shaped and silvered on the back.

• A lever flips the mirror between daytime and nighttime positions.

Daytime Setting

• Light hits the mirror at a small angle of incidence.

• Most of the light is refracted and reaches the silvered back, where it is reflected toward the driver's eyes.

• This provides a clear view of the traffic behind the car during the day.

Nighttime Setting

• Most light penetrates the mirror glass and is refracted.

• A small amount of light is reflected toward the driver’s eyes, reducing the intensity of headlights.

• Most of the light penetrates, refracts, hits the silvered back, and is reflected away from the driver’s eyes.

Large Angles of Incidence

• When underwater, light coming from directly above or at a small angle of incidence penetrates the surface and is visible.

• As the angle of incidence increases, more light reflects off the water, and less is visible.

• Nearly all light from large angles of incidence is reflected and never reaches the diver, creating the illusion of light coming through a hole.

Refraction: Water to Air

• Standing in shallow water, you can see objects underwater that are close to you.

• As you look farther away, objects become more difficult to see.

• At a significant distance, you cannot see anything below the surface due to refraction and reflection effects.

The Critical Angle

• For an object underwater to be visible, light must reflect off it and travel to your eyes.

• When light travels from water to air, the refracted rays bend away from the normal.

• As the angle of incidence increases, the angle of refraction increases more rapidly.

• Critical Angle: The angle of incidence that produces a refracted ray at an angle of 90° from the normal, symbolized by $∠c$. At this angle, no light passes into the second medium.

Definition:

• The critical angle $∠c$ is the angle of incidence that produces an angle of refraction of 90°.

Total Internal Reflection

• The size of the critical angle depends on the indices of refraction of the two media.

• When the angle of incidence is larger than the critical angle, no refraction occurs; all light is reflected back into the first medium.

• Total internal reflection happens only when light travels from a medium in which its speed is lower to a medium in which its speed is higher.

Definition:

• Total internal reflection is the phenomenon in which incident light is not refracted but is entirely reflected back from the boundary. This occurs when light travels from a medium in which its speed is lower to a medium in which its speed is higher.

Activity 11-3: The Fountain of Light

• Objective: Observe total internal reflection within a stream of water in a darkened room.

• Materials:

  • Clear plastic bottle

  • Duct tape

  • Thumbtack

  • Masking tape

  • Water

  • Bucket or sink

  • Flashlight

  • Scissors

• Procedure:

  1. Make a small hole in the bottle covered with masking tape.

  2. Fill the bottle with water.

  3. Shine a flashlight through the bottle opposite the hole.

  4. Remove the masking tape and observe the stream of water.

  5. Look for the spot where total internal reflection occurs and measure the critical angle.

  6. Enlarge the hole and repeat.

• Observations:

  • Total internal reflection occurs when light in water hits the water-air surface at an angle greater than 49°.

  • Total internal reflection is more apparent when the stream of water falls far from the bottle.

Changing the Direction of a Light Ray

• A glass prism can change the direction of light by creating the conditions for total internal reflection.

• The critical angle between glass and air is less than 45°.

• Light hitting an inner surface at exactly 45° will be totally reflected inside the glass.

Isosceles Right Triangle Prism

• When light enters perpendicular to one of the short sides:

  • The angle of incidence is zero, so there is no refraction.

  • Light travels straight through to the long side.

  • At the long side, the angle of incidence is 45°, so the angle of reflection is also 45°.

  • The total change in direction is 90°.

• When light enters perpendicular to the long side:

  • It is reflected off both short sides, changing direction by 90° each time.

  • The total change in direction is 180°.

• When light enters the long side at any angle, it is reflected back in the direction it came from.

Applications of Total Internal Reflection

Binoculars

• Binoculars use total internal reflection to lengthen the path of light and move it to the side.

  • This is important for magnification and image clarity.

Retroreflectors

• Retroreflectors change the direction of light by 180°.

• They are used on bicycle reflectors, so light from headlights is always reflected back to the car.

Optical Fibres

• Optical fibres have revolutionized communication, including the Internet.

• Structure:

  • Glass core surrounded by optical cladding.

  • The cladding has a lower index of refraction than the core to facilitate total internal reflection.

• How it works:

  • Light enters the end of the fibre almost parallel to the axis.

  • It hits the boundary between the core and cladding at an angle larger than the critical angle.

  • Light is totally internally reflected along the fibre until it reaches the other end.

• Fibre bundles:

  • Individual fibres are coated for strength and protection.

  • Groups of fibres are bundled together into cables.

  • Cables can be metres to kilometres long.

Fibre Optics in Telecommunications

• Fibre optic cables are replacing copper wire cables because:

  • Signals are not affected by electrical storms.

  • Fibre optics cables can carry more signals with less energy loss.

  • Fibre optics cables are smaller and lighter.

Fibre Optics in Medicine

• Optical fibre bundles have transformed surgical procedures.

Endoscopes

• Endoscopes use optical fibre bundles.

  • One bundle carries light into the surgical area.

  • Another bundle carries an image back to a monitor.

• Benefits:

  • Smaller incisions and shorter recovery times.

  • Reduced risk of infection.

Diagnostic Uses

• Doctors use endoscopes to diagnose problems, such as ulcers or cancer.

• They can view the inside of the stomach and take tissue samples.