Chapter-3 Optical instruments

Assistant professor- Rupali Kharat.

Department of physics

optical instruments

Most optical instruments involve just the laws of reflection

and refraction – microscope, telescope etc

some optical instruments make use of the wave-nature of

light, such as the interferometer

In this chapter we consider some optical instruments,

starting with the eye

quiz (extra ordinary)

unpolarized light with intensity I0 is projected onto a

polarizer whose polarization axis is at 450 relative to the

vertical axis. The light that passes through is then

projected onto a second polarizer with a polarization axis

that is at 900 relative to the vertical axis. Which of the

following is true?

a) the intensity after the first polarizer is the same as I0

b) the intensity after the second polarizer is 0

c) the intensity after the second polarizer is smaller than I0,

but larger than 0.

d) the intensity of the light after the second polarizer is

larger than the intensity after the first polarizer

the eye

the eye essentially consists of a lens that focuses light on

the retina. The ciliary muscles are used to change the

curvature of the lens and hence the focal length.

the eye II

when the ciliary muscles are relaxed, an object at infinity is focused

onto the retina. The focal length is about 1.7 cm.

optometrists define the power P of a lens in terms of diopters

D=1/f (f in m, D in diopters 1/m)

the typical eye has a power of 1/0.017 m=59 diopters

the far-point

The largest distance that can clearly be seen is called the far-point FP.

a good human eye can visualize objects that are extremely far away

(moon/stars) and the far point is then close to infinity.

nearsightedness (myopia)

In case of nearsightedness, the

far-point is much smaller than

infinity for example because

the eyeball is elongated.

on object placed at infinity is

focused in front of the retina.

this can be corrected using a

diverging lens…

the near point

The near-point is the closest distance in front the eye that

a person is capable of focusing light on the retina

the near-point for a normal person is about 25 cm, making

it hard to focus an object closer to you eyes than that.

farsightedness (hyperopia)

happens when the near-

point is much larger than

25 cm.

it becomes hard to see

objects nearby since the

eye muscles cannot

accommodate it.

it can be corrected using a

converging lens (reading

glasses)

10

simple magnifier normal eye cannot focus if the object

distance < near point (NP)

therefore, the maximum subtended angle

equals:

0=h/NP=h/(25 cm)

(assumed that tan= : small

if we put the same object in front of a

converging lens with p<f, a virtual upright

image is created

1/p+1/q=1/f with p<f

q=pf/(p-f) with p<f so q: negative

M=himage/hobject

=-q/p=-f/|f-p| with p<f so M>1

maximum subtended angle now equals:

I=h’/q=h/p

angular magnification m=I/0

m=I/0=(h/p)/(h/NP)=NP/p

eye

NP

0h

h’h

p

q

f

the best result is obtained

if the image is at infinity

(eye relaxed). to do so p=f

and m=NP/f

the microscope…

…uses two converging lenses with focal lengths f1 and f2 with f2>f1moreover, L>>f2For lens 1: p1 is chosen such that q1~L (image 1 will appear just within F2)

This happens when p1~f1so: M1=-q1/p1=-L/f1Lens two then acts as a magnifying glass with m2=NP/f2=25/f2The magnifying power is defined as m=M1m2=(-L/f1)(25/f2)=-25L/(f1f2)

(all units in cm), usually written as: m=-25L/(fOfe) (inverted!)

with O for objective and e for eyepiece

L

a telescope

a telescope is very similar to a microscope except that the lenses are slightly differently configured:

light comes in (from a star) almost parallel. It is focused at the focus point fo of the first converging (objective) lens.

this image becomes the object for the second converging (eyepiece) lens and is place just at the focal length fe of that lens.

o

size of image of

objective lens: hi

e

L

PHY232 - Remco Zegers - optical instruments

resolution

resolution: the ability of an optical system to distinguish

between two closely spaced objects

resolution is limited by the wave nature of light: when light

passes through a slit, it is diffracted and thus smeared out.

if the angular separation becomes two small, objects

become hard to distinguish

rayleigh’s criterion

two images are just resolved if rayleigh’s criterion is fulfilled.

Rayleigh’s criterion: the central maximum of image A false into the first minimum of image B

first diffraction minimum: sin=/a with A the slitwidth

images separated by a minimum angle min=/a can just be resolved

if the aperture is circular with diameter D: min=1.22/D

The Michelson Interferometer

moveable

1

2 3

4

5

6

1) monochromatic light is incident on mirror

2) light travels to moveable mirror and is…

3) reflected

4) some light is also passed through and is …

5) reflected

6) beam 3) and 5) interfere and make an

interference pattern

7) by moving the moveable mirror, the path

length difference can be varied

Michelson interferometermoveable

1

2 3

4

5

6

the compensator servers to make sure that the light going to either branch travels the same distance through the glass.

The path length difference D=2d23-2d45

If the movable mirror moves by /2, D changes by and the interference pattern is shifted by 1 fringe.

Insertion of a material with index of refraction n in path 2-3 will also make a path length difference, and by observing the change in the interference pattern, one could determine n

more about this in the last week’s lecture on relativity…