This document provides summaries of key formulas and concepts in ray optics, including: 1) Snell's law describes the relationship between the refractive indices of two media and the angle of incidence and refraction. Total internal reflection occurs when light travels from an optically dense medium to a less dense one at an angle greater than the critical angle. 2) Formulas are provided for mirror and lens formulas, linear magnification, magnification of microscopes and telescopes, and resolving power. 3) Refraction through a prism depends on the angle of incidence and angle of minimum deviation. Dispersion and angular dispersion describe how prisms separate white light into constituent colors.

1. Important
Ray Optics
Formulas

2. Mirror Formula

3. Relation between Refractive indices
According to Snell's law
By Snell’s law

4. Refractive index

5. Real depth and Apparent depth

6. 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.

7. Necessary conditions for Total Internal Reflection
a)Light must travel from denser to rarer medium
b)The angle of incidence (in denser medium)
must be greater than the critical angle
where

8. Refraction at Spherical Surfaces
1. When light goes from rarer to denser medium through a spherical surface
Having radius of curvature R.
2.When light goes from denser to rarer through a spherical surface

10. The Lens Formula

11. Linear Magnification
For mirrors :
For lenses :

12. (Take care that f is in meter)
* For thin lenses in contact :

13. * Thin lenses placed at a distance d:
(For two lenses)

14. Refraction through a prism

15. 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)

16. 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 :

17. 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

18. 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.

19. Optical Instruments

20. Simple Microscope
* Magnifying Power when image is formed at least distance of
distinct vision .
* Magnifying power when final image is formed at infinity

21. 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

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

23. Reflecting Type telescope
It was designed by Newton. Used for observing distant stars.
*In normal adjustment , magnifying power of a reflecting type
telescope is :

24. 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

25. Thank You for Viewing It.