Ray optics

Physics http://www.sigmaprc.in

Optical instruments

Ray optics

Physics http://www.sigmaprc.in

Visual angle and magnification

Size of object as sensed by eye is determined the angle subtended by the object atthe eye. This angle is called visual angle.

For a body of certain size, a large visual angle is subtended by it when it is close tothe eye than when it is far away from eye. A larger visual angle enables us to lookinto the details of the object and this is called magnification.

Simulationhttp://www.sigmaprc.in

Ray optics

Physics http://www.sigmaprc.in

Simple microscope ( image formed at near point ) Simulationhttp://www.sigmaprc.in

A simple microscope consists of a single convex lens.

Object is located between focal point and optic centre.

An enlarged, virtual and erect image of object is formed by the lens.

Visual angle subtended by image ( formed at near point ) is more than the visualsubtended by object ( if located at near point).

Optic centre OObject ABImage A’B’

focal length fObject distance u

Image distance D

Object angle b

Image angle a

Ray optics

Physics http://www.sigmaprc.in

Simple microscope ( image formed at near point )

Magnification

Using lens formula

1 1 1 =

f v u

vm =

ui

1 1 1 =

u v f ii

1 1m = v

v f

When image is formed atnear point, v = D therefore

1 1m = D

D f

1D

m = f

Using sign conventionfor the given case

1D

m = f

Ray optics

Physics http://www.sigmaprc.in

m =

i

o

Simple microscope ( image formed at infinity )

Hm =

h

From the figure, angularmagnification can be obtainedusing visual angle subtendedby object and the image.

Dm =

f

Ray optics

Physics http://www.sigmaprc.in

Magnification at near point is 1 more than the magnification at infinity.

Eye is more relaxed when the image is formed at infinity and this situation ispreferred.

1D

m = f

Magnification at near pointD

m = f

Magnification at infinity

Magnification of a simple microscope is limited by the focal length of lens. Lesserfocal length leads to larger magnification. However lesser focal length requiressmaller radius of curvature which in turn leads to reduced size of aperture andincrease in aberration.

Due to this limitation a combination of lenses is used to obtain largemagnification. This combination is called compound microscope.

Simple microscope

Ray optics

Physics http://www.sigmaprc.in

Compound microscope( construction )

It consists of twoconvex lens placedcoaxially.

Lens closer to objectis called objective

Lens closer to eye iscalled eyepiece.

Objective is of smallfocal length andaperture.

Eyepiece is of largefocal length andaperture.

Distance between objective and eyepiece can be adjusted using rack-pinionarrangement.

Ray optics

Physics http://www.sigmaprc.in

Focal length of objective fo

Focal length of eyepiece fe

Object distance ( from objective ) u

First image distance (from objective ) v

Final image distance (from eyepiece ) D

Object ABFirst image A’B’

Final image A’’B’’

Compound microscope(terms )

Ray optics

Physics http://www.sigmaprc.in

Object is placedbeyond focal pointof the objective

A magnified realinverted image isformed by theobjective

Distance of firstimage, from theeyepiece is lessthan the focallength of eyepiece

Image formed by the eyepiece is large, erect and virtual image

Compound microscope( working )

Ray optics

Physics http://www.sigmaprc.in

h' Lm =

h f o

0

o em = m m

e

L Dm =

f f

0

1

Compound microscope( magnification )

1D

m = f

e

e

i

iii

L : Tube length i.e. distance between 2nd focal point ofobjective and 1st focal point of eyepiece ( note that objectis close to objective and first image is close to eyepiece )

ii

Magnification of objective

Magnification of eyepiece

Total magnification

Ray optics

Physics http://www.sigmaprc.in

Astronomical telescope( construction )

It consists of two convex lensplaced coaxially.

Lens facing the object is calledobjective

Lens closer to eye is calledeyepiece.

Objective is of large focallength and aperture.

Eyepiece is of small focallength and aperture.

Distance between objectiveand eyepiece is adjusted usingrack-pinion adjustment.

Ray optics

Physics http://www.sigmaprc.in

Astronomical telescope( Normal adjustment )

Image (A’B’) formed byobjective is in the focal planeof objective

This image (A’B’) acts as anobject for the eyepiece.

Distance between the lensesis adjusted so that the finalimage is formed at infinity

Ray optics

Physics http://www.sigmaprc.in

Astronomical telescope( Normal adjustment )

Magnification ( angular )is given by

βm

α

β

αm

tan( )

tan( )

f

fm o

e

A'B'

A'B'

f

fm o

e

Length of the telescope ( tube length ) is given by

L f f o e