Ray Optics Formulaes

Important Ray Optics Formulas

Mirror Formula

Relation between Refractive indices

By Snell’s law

According to Snell's law

Refractive index

Real depth and Apparent depth

Total Internal Reflection and Critical angle

Total internal reflection occurs when light is passing through a medium (call it 1) like glass or plastic with an index of refraction n1. Outside this material is a medium like air (call it 2) with an index of refraction n2. For certain angles of incidence for light striking the interface and going from medium 1 to medium 2, light will not pass through the interface, but will be totally reflected inside medium 2. This occurs primarily when the light strikes a glancing blow on the interface. For a thin material of medium 2, like a fiber, these angles will always be small, and the light will stay inside the fiber. This process, called total internal reflection.

Necessary conditions for Total Internal Reflection

a)Light must travel from denser to rarer mediumb)The angle of incidence (in denser medium) must be greater than the critical angle where

Refraction at Spherical Surfaces

1. When light goes from rarer to denser medium through a spherical surfaceHaving radius of curvature R.

2.When light goes from denser to rarer through a spherical surface

THE LENS MAKER’S FORMULA

The Lens Formula

Linear Magnification

For mirrors :

For lenses :

Power of a lens

(Take care that f is in meter)

* For thin lenses in contact :

* Thin lenses placed at a distance d:

(For two lenses)

Refraction through a prism

When the angle of incidence is such that the refracted ray inside the prism is parallel to the base of the prism , the prism is said to be in a position of minimum deviation. Under this condition

From Snell’s law

(where is angle of minimum deviation)

Dispersion of light

Splitting up of white light into its constituent colours on passing through a medium is called dispersion of light and the medium of dispersion is called dispersive medium. # Dispersion of light is owing to the fact that velocity of light of different wavelengths is different in a material medium .# Angle of dispersion depends upon angle of prism and material of prism.# According to Cauchy’s Formula :

Angular Dispersion

For white light it is equal to the difference in the angle of deviation fro two extreme colours i.e., violet and red.

*Angular separation between violet and red wavelengths/colours produced by a prism is called angular dispersion.

*Mathematically

Dispersive Power

The ratio of angular dispersion to the angle of deviation for the mean wavelength (yellow colour) is called dispersive power of the material of the prism. Thus dispersive power , ω can be written as :

* Dispersive Power is independent of angle of prism but dependent upon material of prism.

Optical Instruments

Simple Microscope

* Magnifying Power when image is formed at least distance of distinct vision .

* Magnifying power when final image is formed at infinity

Compound Microscope

(*Two conves lenses are used. *Aperture and focal length of objective lens are smaller as compared to those of eye piece)

#When final image is formed at infinity

#When final image is formed at least distance of distinct vision

Astronomical Telescope

*When final image is formed at distance of distinct vision , the magnifying power is given by

*When final image is formed at infinity (telescope is said to be at normal adjustment) , the magnifying power is given as

*Objective is a convex lens of large aperture and large focal length whereas eye piece is also a convex lens of smaller focal length

Reflecting Type telescope

It was designed by Newton. Used for observing distant stars.

*In normal adjustment , magnifying power of a reflecting type telescope is :

Resolving Power•It is the reciprocal of limit of resolution.•It is an ability of an instrument to resolve the images of two points lying close to each other . •Resolving power of a microscope is :

Θ is the half angle subtended on to the objective lens by the cone of light from the point object under observation . D is the minimum distance between the two point object under observation.* d is the minimum distance between the two point objects for which they can be seen as separate objects through a microscope

*Resolving power of a telescope :

*Where D is aperture of objective of the telescope or diameter of the objective lens.*dΘ is the angle subtended at the objective by the two point objects

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