1. The power of a lens is defined as the reciprocal of the focal length in unit meter.
   
   
2. Important Note: f is in meter
3. The unit of power is diopter (D).
4. The relationship of the power with the thickness and types of lens are shown in the diagram below.

Thinner – Lower Power – Longer Focal Length


Thicker – Higher Power – Shorter Focal Length

 

1. There are 2 types of lenses, namely the
   1. Convex lens
   2. Concave lens
2. Convex lenses are thickest through the middle, concave lenses are thickest around the edge, but several variations on these basic shapes are possible, as shown in figure 1. 
3. Light rays passing through a convex or converging lens are bent towards the principal axis, whereas rays passing through a concave or diverging lens are bent away from the principal axis.

Figure 1: Convex Lenses


Figure 2: Concave Lenses

Important Terms

Optical centre, P	Light passing through the central block emerges in the same direction as it arrives because the faces of this block are parallel. P marks the optical centre of the lens.
Principle Axis	The principle axis of a lens is the line joining the centres of of curvature of its surfaces.
Principle focus, F	The principle focus of a lens is the point on the priciple axis to which all rays originally parallel and close to the axis converge, or from which they diverge, after passing through the lens.
Focal length, f	The focal length of a lens is the distance between the optical centre an the principle focus.

Rays of light can pass through a lens in either direction, so every lens has two principal foci, one on each side of the optical centre.

 

Mirage

Rain Bow

 

The Equation Relates the Critical angle (c) with the Refractive Index

The critical angle can be calculated by using the following equation:

Requirements for Total Internal Reflection to occur.

1. The light ray must propagate from an optically denser medium to an optically less dense medium.
2. The angle of incident must exceed the critical angle.

 

 

1. In figure (a) above, the light ray is refracted away from the normal when moving from denser medium to less dense medium.
2. Figure (b) shows that, at a specific angle, the light ray is refracted 90o from the normal. It is refracted so much that it is only just able to leave the water. In such condition, the incident angle is called the critical angle.
3. The critical angle is the angle of incident in an optically denser medium for which the angle of refraction is 90°.
4. In figure (c), the light ray strikes the surface at an angle of incidence greater than c. There is no refracted ray; the surface of the water acts like a perfect mirror, and the ray is said to have been totally internally reflected.

 

 

1. The bending of light can give you a false impression of depth.
2. Figure to the left shows two rays of light leaving a point on the bottom of a swimming pool.
3. The rays are refracted as they leave the water. To the observer, the rays seem to come from a higher position, and the bottom looks closer to the surface than it really is.
4. The real depth of the water and its apparent depth are marked on the diagram. These are related to the refractive index of the water by the following equation:

      or    

Summary:

Refractive index

 

 

Bending of Object in a Glass

A straw in a glass with water looks bended or broken. This is due to refraction of light

Shallower Swimming Pool

A swimming pool appears shallower than it actual is. This is because the light from the pool is refracted away from the normal when moving from water to the air.

Atmospheric Refraction and Setting sun

The setting sun looks oval in shape because the light from the sun is refracted at different rate when passes through the atmosphere.

Twinkling Star

The light of stars is refracted when passes through different region in the atmosphere. The angle of refraction varies a little from time to time. As a result, the stars look twinkling.

 

 

1. The value of  sini/sinr is called the refractive index of the medium and it gives you an indication of its light-bending ability.
   
2. In SPM, when we say “refractive index”, what we mean is the absolute refractive index of a substance. The absolute refractive index of a substance is the refractive index where light ray travels from vacuum (or air) into the substance.

Refractive Index and the Speed of light

or

( Note that the greater the refractive index of a medium, the lower is the speed of light. The more light is slowed, the more it is bent. )

 

1. The incident and refracted rays are on opposite sides of the normal at the point of incidence, and all three lie in the same plane.
2. The value of sini/sinr is constant for light passing from one given medium into another. This is known as Snell's law.

 

1. Light rays are bent when they pass at an angle in or out of materials such as glass and water. The effect is called refraction.
2. Light passing into an optically denser medium is bent towards the normal; light passing into an optically less dense medium is bent away from the normal.
3. Materials such as glass, water and paraffin are said to be optically denser than air.