# Light and EM spectrum Ed excel

### Light:

• Light is a form of electromagnetic radiation that travels in waves.

• It exhibits both wave-like and particle-like properties, known as wave-particle duality.

### Reflection of light

`Basics:`

• The normal line is an imaginary, dotted line exactly 90 degrees to the surface.

• The incident ray is the incoming light ray.

• The angle between the incident ray and the normal is the angle of incidence.

• The angle between the reflected ray and the normal is the angle of reflection.

• A beam is a stream of light made up of multiple rays.

• A ray is the direction of the path in which light is travelling.

### Laws of reflection:

#### First law of reflection

• The incident ray, the normal and the reflected ray all lie in the same plane (they're all on the same flat surface).

#### Second law of reflection

• The angle of incidence is equal to the angle of reflection (<i = <r).

### Drawing reflection of light

• Draw the normal 90 degrees to the surface (make sure it's dotted).

• Measure the angle of incidence.

• Draw the reflected ray on the opposite side of the normal at the same angle (as angle of incidence = angle of reflection).

Always measure the angle from the normal to the surface, never the base. For example, here, 60 degrees is not the angle of incidence because it's not from the normal.

Image produced by a mirror is always:

• virtual

• upright

• laterally inverted

• same size as the object

• opposite side of the mirror as the object

### Regular and irregular reflections:

• If a beam of light falls on a plane mirror, regular reflection occurs.

•  In a regular reflection, the normal lines are the same, so the light rays coming parallel are reflect parallel to each other (clear image).

• If a beam of light falls on an irregular, rough surface, irregular (diffuse) reflection occurs.

• Because of the irregular surfaces, the normal lines are all different.

• The light rays coming parallel are not reflected parallel due to different normal lines (crooked image).

### Refraction of light:

• Refraction is the change in speed of light as it travels from one medium to another of different optical densities.

• Optical density is how much a material can slow down light.

• It's the bending of light due to change in speed as it travels from one medium to another, which depends on the optical density of the medium.

• Refraction of light depends on frequency. The greater the frequency, the larger is the bending of light.

• When light enters an optically denser medium, its speed, wavelength, and angle with the normal decrease. Frequency unchanged.

• When it enters an optically less dense medium, its speed, wavelength, and angle with the normal increases. Frequency unchanged.

• When it enters normal to the surface, its speed and wavelength do change, but the angle doesn't (there's no angle when this happens).

• The speed of the light still experiences a change, it still decreases because refraction is the change in speed of light as it travels from one medium to another due to differing optical densities, in this case, refraction still occurs, there's just no change in direction.

• When light travels through a more dense medium, the refracted ray bends towards the normal.

• When light travels through a less dense medium, the refracted ray bends away from the normal.

### Laws of refraction:

#### - First law

• The incident ray, the normal and the refracted ray all lie in the same plane.

#### - Second law

• The ratio of sine of i to the sine of r is the constant and equals to the refractive index of the refracting medium:

n = sin i/sin r, where,

n = refractive index

i = angle of incidence

r = angle of refraction

• n and r must be of the same medium to apply 2nd law of refraction.

• Denser medium to less dense medium:

n = sin r / sin i Less dense medium to denser medium:

n = sin i / sin r

• If the refractive index of water (n) is 1.2, and it's 1.44 for glass, glass will refract light more than water.

• In terms of speed, n = speed of light in vacuum/speed of light in medium.

### Critical angle:

• The angle of incidence at which the angle of refraction becomes 90 degrees is the critical angle.

• Increasing the angle of incidence increases the angle of refraction and partial reflection.

• At a certain angle of incidence, the angle of refraction becomes 90 degrees.

• Increasing the angle of incidence any further will cause total internal reflection, so this is boundary.

• Remember that it's the angle of incidence that's critical, NOT the 90 degrees angle of refraction.

• If the angle of incidence is increased beyond the critical angle, all the light will be reflected back into the medium. This reflection is called total internal reflection.

• For total internal reflection, light must travel from a denser medium to a less dense medium.

• The angle of incidence must be greater than the critical angle.

• To find the refractive index of a medium when critical angle is given,

n = 1/sin c, where:

n: refractive index

c: critical angle

### Dispersion of Light

• When light is passed through a prism, it disperses into 7 colors due to refraction

• The higher the frequency, the greater the bending of light

• Red has the lowest frequency, so bends the least

• Violet has highest frequency, so bends the most

• Light of one color (hence single frequency) is called monochromatic

### Electromagnetic spectrum

• EM waves form when electric and magnetic fields interact

• Gamma rays have the highest frequency, hence are the most energetic and dangerous (energy is directly proportional to frequency)

• EM waves are transverse, can travel in vacuum, and have the same speed in it i.e 3.0x10^8 m/s

• The obey the laws of reflection and refraction

• Can be emitted and absorbed by matter

• Can transfer energy

• Light is a part of the EM spectrum and not the EM spectrum itself

### Wave-particle Duality:

Electromagnetic radiation exhibits both wave-like and particle-like properties, as demonstrated by phenomena such as the photoelectric effect and Compton scattering.

### Thin lenses:

• Converging (convex) lenses converge the light rays passing through it at a point.

• Diverging (concave) lenses diverge the light rays passing through it at a point.

#### Characteristics of a lens:

1. Optical centre (O) is the geometric centre of the lens. Any light ray passing the optical centre passes straight, unchanged.

2. Principal axis is an imaginary horizontal line passing through the optical centre. All light rays travelling parallel to the principal axis converge at a common point.

3. Principal focus (focal point) is the point at which incident parallel rays meet after passing through the lens.

- If light rays approach diverging, they converge beyond the focal point.

- If they approach converging, they'll converge before the focal point.

- Light rays coming from the focal point become parallel to the principal axis after the lens.

4. Focal length is the shortest distance between the optical center and the focal point.

5. Focal plane is a plane at which light rays converge after passing the lens

### Drawing a ray diagram:

Draw a principal axis and position the lens on it

Mark the focal points on both sides of the lens, label it 'F'

Double the distance of 'F' from the optical center will be the 2F, mark that

Draw the object on the principal axis on the mention location and height

Draw 2 light rays from the top of the object: the first will be parallel to the principal axis and converge at 'F'; the second will pass through the optical center, unchanged and straight throughout

Draw the image where the two light rays intersect

### Short-sightedness

• One is able to see near objects clearly, but distant objects are blurred

• Light rays converge before reaching the retina

• A diverging lens is used so light rays reach the eye and focus on the retina to make a clear image

### Long-sightedness

• Distant objects are clearer than those near

• Light rays converge beyond the retina

• A convex/converging lens is used so that the light rays meet at the retina