Labs: Refractometry, Microscope, Measuring Devices

Question 1

What was determined in the refractometry experiment?

And how?

Answer 1

• refractive indices of several glycerol solutions of known concentration were measured
• the data was used to make a concentration vs. refractive index graph (linear relationship)
• unknown concentrations of 2 glycerol solutions were determined by measuring their RIs and using this graph

Question 2

What is absolute index of refraction?

Relative index of refraction?

Answer 2

Absolute - speed of light in vacuum divided by speed of light through given medium (n₁ = C/C₁)

Relative - ratio of indices of refraction of 2 media (n₁/n₂)

Question 3

What is refraction?

Answer 3

a change in the direction of propagation of light that occurs when the light strikes a boundary surface between two media at any angle other than perpendicular

Question 4

What is Snell’s Law?

Answer 4

• the ratio of the sines of the angle of incidence and the angle of refraction equals the ratio of the speed of light (V) in the corresponding media
• also equals the index of refraction of the 2nd medium (n₂/n₁)

Question 5

What is the critical angle?

Answer 5

less dense to more dense medium - critical angle is the largest angle of refraction, corresponding to the grazing incident ray

more dense to less dense medium - critical angle is the incident angle which will produce a grazing refracted ray

Question 6

What is a grazing ray?

Answer 6

a ray that is parallel to the interface between 2 media

Question 7

What is total internal reflection?

Answer 7

When an incident ray moving from a more dense toward a less dense medium is of an angle greater than the critical angle, all the light is reflected back into more dense medium.

Question 8

What is dispersion?

What causes it?

Answer 8

• decomposure of white light into its component wavelengths
• caused by the dependence of refractive index on wavelength

Question 9

How is dispersion dealt with in the refractometer?

Answer 9

The compensator is a compound prism of two Amici prisms which restores white light from its components

Question 10

What is Snell’s Window?

When does it occur?

Answer 10

• a cone of light formed by refracted rays with an aperature angle 2x the critical angle
• occurs as a result of light moving from less to more dense medium from all possible angles of incidence (as in from air into water)

Question 11

What is the equation which relates concentration of solution to index of refraction?

Answer 11

n₁ = n₀ + K * c

n₁ is RI of solution

n₀ is RI of solvent

K is constant (dependent on solute)

c is concentration

Question 12

How does the Abbe refractometer measure the refractive index of a solution?

Answer 12

it determines the position of the shadowline at the edge of the Snell’s window created when light passes through the solution and into a measuring prism of very high refractive index

(this allows determination of the critical angle)

Question 13

What is the general layout of the Abbe refractometer?

Draw it.

Answer 13

• two tubes with eyepieces: one aimed at the prisms and one aimed at a scale
• a mirror reflects light into the two prisms (illuminating and measuring) between which a drop of solution is placed
• scale is connected to prisms via an axis so that when prisms are turned to show the shadowline, refractive index can be read from scale

Question 14

How are the results from the refractometer lab graphed?

Answer 14

Concentration as independent variable on the X axis

Refractive index as dependent variable on Y axis

(shows a linear relationship with direct proportionality)

Question 15

What was the goal of the the microscope measurement?

Answer 15

A sample of frog RBCs diameters were measured using the micrometer

mean, standard deviation, standard error, reference + confidence intervals were determined

Question 16

What is fermat’s principle?

Answer 16

Light will take the path between two points that keeps travel time to a minimum

(ie longer distance in the medium of lower refractive index)

Question 17

What is the optical axis?

Answer 17

a line connecting the centers of curvature of the spherical surfaces of a lens

(in other words, an imaginary line through the center of the lens, perpendicular to its surface)

Question 18

What are converging and diverging lenses?

Their shapes?

Answer 18

Converging - biconvex, focus light onto one point

Diverging - biconcave, scatters light

Question 19

What is focal length?

Answer 19

the distance along the optical axis between the focal point and the principal plane (middle of lens)

Question 20

What is a real vs. a virtual image?

Answer 20

real - an inverted image created on the opposite side of a lens from its source object which can be projected onto a screen

virtual - an upright image created on the same side of a lens as its source object which can not be projected onto a screen

Question 21

What is the focal point?

Answer 21

the point at which a converging (biconvex) lens focuses light

Question 22

In a simple image formation diagram, what are the names and paths of the 3 main rays coming from an object point?

Answer 22

1. parallel ray - parallel to optical axis, deflected through focal point on opposite side
2. central ray - straight through center of lens
3. focal ray - through proximal focal point, deflected parallel to optical axis

Question 23

What is the lens makers equation?

Answer 23

f is focal length

n is relative RI of lens

R_{1 & 2} are the radii of curvature of the lens (negative if concave)

Question 24

What are the five scenarios of an object’s distance from the lens in relation to once (F) and twice (2F) the focal point ?

What kind of image does each produce?

Answer 24

1. Closer than F - virtual, upright, magnified
2. At F - virtual, upright, at infinity (refracted rays are parallel)
3. Between F and 2F - real, inverted, magnified
4. At 2F - real, inverted, same size as object
5. Beyond 2F - real, inverted, diminished

Question 25

How is the **magnification** of a lens determined?

Answer 25

it is the ratio if the image size to object size (or image distance to object distance) M = I/O = i/o

Question 26

What is the **lens equation**?

Answer 26

Question 27

Describe the path of light from a specimen to the observer in a simple light microscope, considering just the two main lenses.

Answer 27

* light reflects from the object (between F and 2F) through the **objective lens** to form a *real, inverted, magnified image* * the **eyepiece lens** then uses this **"intermediate" image** as an object (at \< F) to form a *virtual, inverted, magnified image*

Question 28

Draw the diagram of how a specimen is magnified by a simple light microscope.

Answer 28

Question 29

How can the eyepiece scale of the microscope be calibrated?

Answer 29

Using a stage micrometer with known distance between marks * line up stage micrometer and eyepiece scale * pick length of eyepiece scale where marks align with stage micrometer * divide known length between stage micrometer marks by number of eyepiece units to get the **calibration factor**

Question 30

What is standard error vs. standard deviation?

Answer 30

**standard error ** - the standard deviation of the sample mean from the population mean **standard deviation** - the amount of variation of a sample of data from the average value

Question 31

What is reference interval vs. confidence interval?

Answer 31

**reference interval ** - mean plus or minus 2 times standard deviation **confidence interval** - mean plus or minus 2 times standard error

Question 32

What is **Huygen's Principle**?

Answer 32

waves propagate such that each point on a primary wavefront is the source of spherical secondary wavelets with the same speed and frequency

Question 33

What is **interference**? What are the two kinds of it?

Answer 33

interference is the process that occurs when two waves meet each other ## Footnote **constructive** - two waves in phase (peak aligned with peak) will combine and strengthen each other **destructive** - two waves out of phase (peak aligned with trough) will cancel out (if of equal amplitude)

Question 34

What is **Abbe's Principle**?

Answer 34

an optical system can resolve only the details of a specimen which diffract light such that at least the 1st order diffraction maxima contribute to image formation

Question 35

What is an optical grating? What are two different kinds of them?

Answer 35

an object with periodic optical properties **amplitude grating** - transmission properties vary periodically (ex: transparent slits between opaque grating elements) **phase grating** - transmission % of grating remains same, but refractive index (and thus phase of transmitted light) changes periodically

Question 36

What is the **double slit experiment**?

Answer 36

two slits in an optical grating between a light source and screen act as two different sources of secondary wavelets which interfere with one another to create a pattern of light and dark bands on the screen

Question 37

What is the name of the light bands of an interference pattern created by an optical grating? And how are they numbered?

Answer 37

**Diffraction Maxima** - middle is 0th order maximum, next out are 1st order maxima, then 2nd order, etc.

Question 38

What is **Abbe's Formula**?

Answer 38

delta is minimum resolvable distance n is RI of immersion medium omega is half-aperature angle of light entering objective lens

Question 39

What is the **numerical aperature** of an objective lens (in relation the the special microscopes experiment)?

Answer 39

the divisor of the abbe formula (which is the product of the index of refraction of the immersion medium and the sine of the half-aperature angle) ## Footnote **n sin ω**

Question 40

What is the **resolving power** of a microscope? How is it calculated?

Answer 40

- the microscope's ability to create a clear image in which very small details can be distinguished - it is the reciprocal of the limit of resolution equation: **f = 1/δ** f is resolving power δ is minimum resolvable distance

Question 41

What is an **immersion objective** microscope?

Answer 41

an immersion medium of high RI is placed between the specimen and objective lens in order to increase the # of diffraction maxima which contribute to image formation

Question 42

What is a **stereomicroscope**?

Answer 42

a microscope which has two separate objective and eyepiece lenses equipped with prism systems which create upright, unmirrored images that allow for more a more 3D view of the specimen - used in microsurgery

Question 43

What is a **dark field illumination **microscope?

Answer 43

* a special condenser is used which blocks the central beam * the specimen is illuminated from sides by oblique rays * image is formed by diffraction rays * used to observe colloid particles

Question 44

What is a fluorescence microscope?

Answer 44

* light source provides UV and visible excitation & filters are used to select proper wavelength * native/stained specimens absorb light and emit visible fluorescence * staining involves use of fluorescent dyes called **fluorochromes** * can reveal presence of single fluorescing molecule (visible as center of shiny disk)

Question 45

What was the goal of the special microscopes lab? How was it achieved?

Answer 45

to prove Abbe's formula and the relationship between wavelength and resolving power by using a light microscope modified with a monochromatic light source to observe an optical grating

Question 46

How is standard error calculated?

Answer 46

standard deviation divided by sq rt of n