IP Topics

25 July

Snell’s Law Self-Assessment

Seng Kwang Tan GeoGebra, IP3 07 Light 0 Comments

My third applet today is a self-assessment tool for students to practise calculations with Snell’s Law, i.e. $n_1 \sin{\theta_1} = n_2 \sin{\theta_2}$.

The direct link to the applet is https://www.geogebra.org/m/fhmmuhbg

Snell’s law, also known as the law of refraction, describes how light waves change direction as they pass from one medium to another with different refractive indices. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media. This law is fundamental in understanding the bending of light when it moves between materials of different optical densities, such as when light passes from air to water, resulting in phenomena like the bending of a pencil in a glass of water.

When light travels from a medium with higher optical density to a medium with lower optical density,

  1. The light ray bends away from the normal: The “normal” is an imaginary line perpendicular to the interface (boundary) between the two media. As light enters the medium with lower optical density, it slows down, causing it to bend away from the normal.
  2. The angle of refraction is larger than the angle of incidence: The angle of incidence is the angle between the incident ray and the normal, while the angle of refraction is the angle between the refracted ray and the normal. In this scenario, the angle of refraction will be larger than the angle of incidence.

When light travels from a medium with lower optical density to a medium with higher optical density,

  1. The light ray bends towards the normal: As the light enters the medium with higher optical density, it slows down, causing it to bend towards the normal, which is an imaginary line perpendicular to the interface (boundary) between the two media.
  2. The angle of refraction is smaller than the angle of incidence: The angle of incidence is the angle between the incident ray and the normal, while the angle of refraction is the angle between the refracted ray and the normal. In this situation, the angle of refraction will be smaller than the angle of incidence.

When light travels from a medium with a higher refractive index to a medium with a lower refractive index and strikes the interface at an angle of incidence greater than the critical angle, total internal reflection occurs. At this critical angle, the light is entirely reflected back into the higher refractive index medium, with no refraction into the second medium, resulting in the complete internal reflection of the light. This phenomenon is crucial in various applications, such as optical fiber communications and the brilliance of gemstones like diamonds.

Update on 27 Jul 2023: I improved on the rather unpolished applet to adjust the calculations for the object when it is below the boundary between the two media. Also added was an indication for when total internal reflection takes place.

25 July

Where is the Fish? A Refraction Simulation

Seng Kwang Tan GeoGebra, IP3 07 Light 0 Comments

I have seen a few simulations for apparent depth but was not satisfied with them. So I created this from scratch for use in tomorrow’s lesson. The positions of the eye and image of the fish are adjustable. It is more challenging to design for the actual fish to be draggable, so I only could allow the image to be dragged and hence, use it to shift the position of the actual fish.

Direct link to the applet: https://www.geogebra.org/m/kdszgpfg

28 March

Use of System Schema to Visualise Action-Reaction Pairs

Seng Kwang Tan 03 Dynamics, IP3 03 Dynamics 0 Comments

It is a common misconception for students to assume that when a book is placed on a table, its weight and the normal contact force acting on it are action-reaction pairs because they are equal in magnitude and opposite in direction.

While we can emphasise the other requirements for action-reaction pairs – that they must act on two different bodies and be of the same type of force – I have tried a different approach to prevent this misconception from taking root. After reading this article on the use of the system schema representational tool to promote understanding of Newton’s third law, I tried it out with my IP3 students.

The system schema identifies the bodies in a question and represents them with shapes detached from each other to give space to draw the connecting arrows between them. The arrows must be labelled with the type of force, either by coding them (e.g. r for reaction force, g for gravitational force) or in full.

Every force will be drawn as a double-headed arrow between two bodies to represent that they are action-reaction pairs. It is important for students to understand that every force in the universe comes in such a pair, and the system schema can help them visualise that. If there is a force without a partner, it just means the system is not in the frame yet.

The next step to using the system schema is for students to isolate the object in question and draw its free-body diagram. Each force vector in the diagram should be accompanied by a name that includes: 1. the type of force and 2. the subject which exerts that force on the object.

The effectiveness of this method of instruction is clearly presented in the paper mentioned above, as performance on the force concept inventory’s questions on the third law saw an improved average from 2.8 ± 1.2 to 3.7 ± 0.8.