# Geometrical Optics

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# Code(Credit) : CUTM1781(3-1-0)

## Course Objectives

• To study of light and its behavior as it propagates in a variety of media.
• To understand the phenomena of reflection and refraction of light at boundaries between media and subsequent image formation will be dealt with in detail.
• To study the reflections at plane and spherical surfaces and refractions at plane, spherical, cylindrical and toric surfaces.
• To Attention will be given to the system of surfaces and/or lenses and their imaging properties.
• To study the effect of aperture stops on the quality of images, such as blur, aberrations, depth of field and depth of focus.

## Learning Outcomes

• The objective of this course is to equip the students with a thorough knowledge of mirrors and lenses. At the end of this course, students will be able to predict the basic properties of the images formed on the retina by the optics of the eye.

## Course Syllabus

Module 1 (5 Hours)

Nature of light –light as electromagnetic oscillation; ideas of sinusoidal oscillations; amplitude and phase; speed of light in vacuum and other media; refractive index.   Wavefronts–spherical, elliptical and plane; Curvature and vergence; rays; convergence and divergence in terms of rays and vergence; vergence at a distance.  Refractive index; its dependence on wavelength.

Module 2 (6 Hours)

Fermat’s and Huygen’s Principle –Derivation of laws of reflection and refraction (Snell’s law) from these principles. Plane mirrors –height of the mirror; rotation of the mirror.  Reflection by a spherical mirror –paraxial approximation; sign convention; derivation of vergence equation. Imaging by concave mirror, convex mirror.  .

Module 3 (5 Hours)

Reflectivity; transmissivity; Snell’s Law, Refraction at a plane surface. Glass slab; displacement without deviation; displacement without dispersion. Thick prisms; angle of prism; deviation produced by a prism; refractive index of the prism.  Prisms; angular dispersion; dispersive power; Abbe’s number.

Module 4 (4 Hours)

Definition of crown and flint glasses; materials of high refractive index. Thin prism –definition; definition of Prism diopter; deviation produced by a thin prism; it dependence on refractive index.

Module 5 (6 Hours)

Nodal Planes.  Sag formula.  Paraxial approximation; derivation of vergence equation.  Imaging by a positive powered surface and negative powered surface. Refraction by a spherical surface; sign convention; introduction to spherical aberration using image formed by a spherical surface of a distance object

Module 6 (6 Hours)

Thin lens as a special case of thick lens; review of sign convention.  Imaging by a thin convex lens; image properties (real/virtual; erect/inverted; magnified/minified) for various object positions.  Imaging by a thin concave lens; image properties (real/virtual; erect/inverted; magnified/minified) for various object positions.

Module 7 (4 Hours)

Prentice’s Rule.  System of two thin lenses; review of front and back vertex powers and equivalent power, review of six cardinal points.  System of more than two thin lenses; calculation of equivalent power using magnification formula

TEXT BOOK:

1. Subrahmanyan N, BrijLal, A text book of Optics, S. Chand Co Ltd, New Delhi, India, 2003.

REFERENCE BOOKS:

1. Pedrotti L. S, Pedrotti Sr. F. L, Optics and Vision, Prentice Hall, New Jersey, USA, 1998.
2. Keating NM. P, Geometric, Physical and Visual Optics, Butterworth- Heinemann, Massachusetts, USA, 2002.

# Session Plan

## Session 5

Refractive index; its dependence on wavelength.

## Session 6

Fermat’s and Huygen’s Principle –Derivation of laws of reflection and refraction (Snell’s law) from these principles.

https://www.slideshare.net/franceschongg/huygens-principle-45865554?qid=0f927656-90a9-43c0-810a-f705c29a8618&v=&b=&from_search=2

## Session 10

Derivation of vergence equation

## Session 18

Thin prism –definition; definition of Prism diopter;

## Session 19

Deviation produced by a thin prism; it dependence on refractive index

https://www.slideshare.net/bipinkoirala3/real-prism-use-in-ophthalmology?qid=858dc4bc-8072-4e63-a825-33c70cccdc25&v=&b=&from_search=6

Practice 2: Thin Prism – measurement of deviation; calculation of the prism diopter

## Session 24

Spherical aberration using image formed by a spherical surface of a distance object

Practice 3: Image formation by spherical mirrors

## Session 26

Review of sign convention of lense

## Session 28

Image properties (real/virtual; erect/inverted; magnified/minified) for various object positions

## Session 29

Imaging by a thin concave lens

## Session 30

Image properties (real/virtual; erect/inverted; magnified/minified) for various object positions

Practice 4: Construction of a tabletop telescope – all three types of telescopes

https://www.slideshare.net/AqilahRajak/modern-telescope-5ws-1h?qid=78f03b4a-1d64-4146-b3c2-2d9d488b39c1&v=&b=&from_search=16

Practice 5: Construction of a tabletop microscope

## Session 32

System of two thin lenses, review of front and back vertex powers and equivalent power.

## Session 34

System of more than two thin lenses; calculation of equivalent power using magnification formula

Practice 6: Imaging by a cylindrical lens

Practice 7: Imaging by two cylinders in contact

Practice 8: Imaging by a spherocylindrical lens

## Case Studies

### Dr Vijaya Babu Kannipamula

##### Assistant Professor
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Received Ph. D. from the Andhra University, Visakhapatnam, India and qualified State Eligibility Test conducted by Government of Andhra Pradesh. Previously worked as Research Scientist in DST funded project PURSE at Andhra University where the major responsibility involves research and handling of instruments like that SEM-EDS, XRD, ESR, TG/DTA/DSC, FTIR, UV-Visible spectrophotometer, Network Analyzer, HT-Furnace […]