# Evan's Space

## Ring of Fire Solar Eclipse

View from Bishan-AMK Park, Singapore

## Light and sound wave diagram in different mediums with different density

Light and sound are both waves. So both carry energy from one place to another.

Light, which is part of the electromagnetic spectrum, is a transverse wave, It can travel through a vacuum at speed 3.0 x 108 m/s. As the light travels from an optically less dense medium (air) to an optically denser medium (liquid or glass), the light undergoes refraction and bends towards the normal due to a decrease in speed.

Light: Optically less dense medium to denser medium:
– speed decreases
– wavelength shorter
– frequency remains constant

Sound is a longitudinal wave. It requires a medium to pass through and it cannot pass through a vacuum. Opposite to light, as the sound travels from a less dense medium (air) into a denser medium (water or solid), the speed increases.

Sound: Less dense medium to denser medium:
– speed increases
– wavelength longer
– frequency remains constant

Refers to the image below to understand how the waves behave in different mediums.
Click here to revise on the calculation of refractive index for light

## Using Slinky Coil to demonstrate Transverse and Longitudinal Waves

Though slinky coil is commonly used to demonstrate transverse and longitudinal waves, you must not quote it as an example for either of the waves.

• Transverse waves are waves in which the direction of the wave is perpendicular to the direction of the vibration of the particles. Examples are light wave, water wave or all the waves in the electromagnetic spectrum (which light is one of the waves.
• Longitudinal waves are waves in which the direction of the wave is parallel to the direction of the vibration of the particles.  Example is sound wave.

Transverse Waves (slinky coil)

Longitudinal Waves (slinky coil)

Click here to see the simulations of transverse and longitudinal waves.

## Converging Lens Overview

1. Converging lens (convex lens)
Converging lens, also known as convex lens,  is thicker at the centre. Below shows some examples.

In O-level, we learned about symmetrical converging lens. i.e. the curvature of the lens are the same on both sides. As light rays pass through the converging lens, the rays come closer together.

Take note that the bending of light, refraction, takes place on the air-glass boundaries on both sides of the lens (as shown above). But for easy drawing, we draw the bending at the imaginary centre vertical which passes through the optical centre as shown below.

2. The 3 Rays

The following 3 rays are important for us to construct the ray diagram and locate the image. We always draw these 3 rays as they have rules to follow, hence guiding us in our drawing.

Refer to the video below for better understanding of the 3 rays.

3. The 4 Key Scenarios
Depending on the distance of the object to the centre of the lens (object distance u), the kind of image you get varies.

Refer to the video below for the better understanding of how the various images are formed.

3. The Pattern
Besides knowing the 4 key scenarios, it is important to know how the image behaves as the object is moved towards the lens.

In general, as the object (starting from a distance of >2f) moves closer to the lens, the image will move further away from the lens and the size of the image becomes bigger.

But when the object is within a focal length, as it moves closer to the lens, the virtual image moves closer to the lens and it becomes smaller compared to the image previously. But the virtual image is always bigger than the object.

Refer to the video for better visualisation and understanding.

4) Other posts on converting lens:

What is focal length and how to identify

Finding focal length f of the lens (using a mirror and pin practical experiment)

Different converging lens ray diagram questions (must know)

Different ways to have a sharp image formed on the screen

Which distance is the focal lens of the converging lens? Olevel question

## Where is the focal point?

Refer to the diagram (below left) which many are familiar. When parallel rays of light which are parallel to the principal axis enter the lens, the rays bend (refraction), come closer and converge to a point on the principal axis called focal point (F). The distance from the optical centre (C) to the focal point (F) is the focal length (f).

But what if the parallel rays of light entering the lens are not parallel to the principal axis but at an angle as shown on the diagram (below right)?

As you can see, the rays refracted and converge to a point P which is along the focal plane (imaginary vertical line through F and is perpendicular to the principal axis). This is similar to L1 in the question. (Refer to the first section of the video simulation below to reinforce your concept)

How about L2 in the question?

Light is reversible so you can also treat the light rays entering from the right of the lens L2. The parallel rays of light in L2 are at an angle but there is no ray through the optical centre C.

Refer to the video below, as you can see, the parallel rays of light will likewise refract and converge to a point, which is along the focal plane too.

Hence the focal point of both lenses L1 and L2 is at F2. So the answer is Option A.

## Finding focal length f of the lens

A thin convex lens is placed on a plane mirror and an object pin is then moved along the axis of the lens until an image is seen to coincide with the object pin when viewed from above. What is then the distance between the pin and the lens? (Take f as the focal length of the lens)

A     0.5 f            B     1.0 f          C      1.5 f          D      2.0 f

A common mistake is to assume this is the scenario (2nd scenario) where the object is at 2F and the image formed is at 2F, hence the image is the same size as the object, inverted and real. But this is not the case.

Refer to the video tutorial for the explanation.

This set up of the lens with the mirror is using the concept that when parallel light rays (parallel to principal axis) enter the lens, the rays will converge to a point after passing through the lens. This point is called the focal point, F. The distance between F and the optical center of lens is the focal length f. Refer to the diagram below.

When you adjust the object (pin) until both the object and the image coincide even when you move your eye forward or backward perpendicular to the axis, the distance between the optical center and the object (pin) is the focal length f.

At this position, as the rays from the object pass through the lens, due to refraction, the rays converge and becomes parallel to the axis. Due to the mirror, the parallel rays will be reflected back to the lens and then converge to a point that coincides with the object.

Refer to the video on how to get that position.

Before you start the experiment to find the focal length f, there is a fast and easy way to estimate the f. Refer to the video below.

Below is another image of another set-up but with the same concept.

Another similar question below. The answer is Option B