Refraction of Light

Prism

Angle of deviation through a prism      d = i₁ + i₂ –A

                                                          A = r₁ + r₂

 Variation of angle  of incident and angle of deviation

At minimum deviation 

Dispersion of light through a prism

When passing through a prism

·        

•  Violet light deviate most while red light deviate less.
•  Refractive index of violet light is larger  than refractive index of red light.
•  Red light travel faster than any other colour light ( n.v =cont).
•  Frequency is unchanged.
•  Red light has the longest wave length while the violet has the least.            

Lenses

Convex Lens /Converging Lens

Concave Lens / Diverging Lens

Sign Convention

 New Cartesian Sign Convention

·         All distance on the principle axis are measured from optical centre.

·         The distance measured in the direction of incident rays are positive and all distance measured in the direction opposite to that of incident rays are negative. 

Old Cartesian Sign Convention

·         All distance on the principle axis are measured from optical centre.

·       The distance measured in the direction of incident rays are negative  and all distance measured in the direction opposite to that of incident rays are positive.


 
Lens Formula 

Linear magnification 

Power of a lens – P

Combination of lenses

If two lenses having focal length f₁ an f₂ placed in contact the equivalent focal length f,

Since the power of a lens is the reciprocal of the focal length, the equivalent power of the lenses  P can be written as,

 

Human Eye

Functions of human eye :

Iris:

The size of the pupil opening can be adjusted by the movement of the iris, and hence it can control the intensity of light .enters the eye.  The iris is the colored part of the eye - being blue for some people and brown for others.

Cornea:

The eye is essentially an opaque eyeball filled with a water-like fluid. In the front of the eyeball is a transparent opening known as the cornea.  The cornea is a thin membrane that has the dual purpose of protecting the eye and refracting light as it enters the eye.

Ciliary Muscle:

The lens is attached to the ciliary muscles. These muscles relax and contract in order to change the shape of the lens so as to change the focal length. By carefully adjusting the lenses shape, the ciliary muscles assist the eye in the critical task of producing an image on the back of the eyeball.

Important points  about human eye :

Accommodation of eye

The process of changing the focal length of the eye so as to focus the image of objects at different distances on retina which is at a fixed distance from the eye lens, this process is known as the accommodation of eye.

Least distance of distinct vision (D)

The minimum distance from the eye at which an object appears to be distinct is called least distance of distinct vision or near point. The distance is represented by D is about 25cm from the eye. If the object is held closer to the eye than the distance the image formed will be  fuzz and it is uncomfortable for the eye. The location of the near point, however, changes with age

An average person

·         Range of human vision is 25cm to infinity

·         The diameter of the eye ball is 2.5cm

·         Maximum focal length of the eye is 2.5cm

Defects of eye and  correction :

A normal eye can see all objects over a wide range of distances i.e., from 25 cm to infinity. But due to certain abnormalities the eye is not able see objects over such a wide range of distances and such an eye is said to be defective. Some of the defects of vision are

• Hypermetropia or long sightedness
• Myopia or short sightedness
• Presbyopia

Myopia / Short-sightedness :

This is a defect of vision in which far objects appear blurred but near objects are seen clearly. The image is focused in front of the retina rather than on it usually because the eyeball is too long or the refractive power of the eye’s lens too strong. Myopia can be corrected by wearing  concave  lens, these help to focus the image on the retina.

Hypermetropia / Long-sightedness:

This is a defect of vision in which there is difficulty with near vision but far objects can be seen easily. The image is focused behind the retina rather than upon it. This occurs when the eyeball is too short or the refractive power of the lens is too weak. this can be corrected by wearing convex lens , these help to focus the image on the retina.

Presbyopia 

This is a condition arise with age, the eye exhibits a progressively diminished ability to focus on near objects. This is due to loss of elasticity of the crystalline lens, although changes in the lens’s curvature from continual growth and loss of power of the ciliary muscles. Like gray hair and wrinkles, presbyopia is a symptom caused by the natural course of aging.