1. The angular magnitude of an object is the virtual angle at the eye. It is the angle the object subtends at the eye.
2. This angle determines the size of the image (apparent size) formed on the retina and hence governs the apparent size of the object 

 

The Lens Equation

1. The following is the lens equation that relates the object distance (u), image distance (v) and the focal length.
   
2. When using the lens equation to solve problem, it's important to note the positive negative sign of u, v and f.
3. Table below give the conventional symbol and sign for u, v and f.

 

 

m = linear magnification
u = distance of object
v = distance of image
h_i = heigth of image
h_o = heigth of object

 

1. The image formed by a concave lens always has the same characteristics, namely
   1. virtual
   2. upright
   3. diminish
2. Figure below shows the ray diagram for the formation of image of a concave lens.

 

 

Characteristics of the Image Formed by a Convex Lens

1. As with a curved mirror, the position and size of an image can be found by drawing a ray diagram.
2. Any two of the following three rays are sufficient to fix the position and size of the image.
3. The characteristics, position and size of the image formed by a convex lens depends on the object distance (u) relative to the focal length (f)

Position of Object: u > 2f

Characteristics of the Image: Real, inverted, diminish
Distance of image: v < 2f

Position of Object: u = 2f

Characteristics of the Image: Real, inverted, same size
Distance of image: v = 2f

Position of Object: f < u < 2f

Characteristics of the Image: Virtual, uprigh, magnified
Position of image: at the same side of the object

 

Rules for Drawing Ray Diagram for Convex Lenses

1. A light ray passes through the optical centre of the lens will not be refracted.
   
   
2. A light ray parallel to the principle axis of the lens will be refracted passes through the principle focus.
   
   
3. A light ray passes through principle focus will be refracted parallel to the principle axis.
   
   

Rules in Drawing Ray Diagram for Concave Lens

1. A light ray passes through the optical centre of the lens will not be refracted.
   
2. A light ray parallel to the principle axis will be refracted away from the principle focus
   
3. A light ray moving towards the optical centre will be refracted parallel to the principle axis.
   

 

 

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.