Physics 1230 Light and Color Fall 2007 Tues., Nov. 8, 2007

Solutions to Exam #2 White version 1

This exam will be worth 100 points. There are 10 multiple choice questions worth 4 points each and 3 problems worth a total of 60 pts. Please put your answers to the multiple choice probems on a properly filled out bubble sheet. There will be no partial credit for the multiple choice problems. Your answers to the problems should be on this exam (not the bubble sheet) in the space provided.

Your full name:
Last ______________________________________________________________
First and middle ____________________________________________________

Equations

Lens eqn: 1/f = 1/x_o + 1/x_i

f = focal length of lens (positive for convex converging lens, negative for diverging lens)

x_o = distance from center of lens to object

x_i = distance from center of lens to image (positive if on opposite side of lens from object, negative if on same side as object)

Magnification eqn: M = s_i/s_o = -x_i/x_o

s_i = size of image (perpendicular to axis), s₀ = size of object (perpendicular to axis)

Relationship between frequency and wavelength of light: l·n = c

l = wavelength, n = frequency, c = speed of light (3 x 10⁸ m/s in empty space)

Bending power of a lens: P = 1/f

P = power in diopters, f = focal length of lens in meters

Combined power of two thin lenses (labeled 1 and 2) in contact: P₁ + P₂ = P

P₁ = power of lens 1; P₂ = power of lens 2; P = power of combined lenses

f-number (f/stop) = (focal length of lens)/(diameter of lens opening at that f/stop)

Metric system distances: 100 cm = 1 m, 10 mm = 1 cm, 25.4 mm = 1 inch

Wavelength colors:

Violet	Blue	Green	Yellow	Orange	Red	Infrared
400 nm	460 nm	530 nm	575 nm	600 nm	650 nm

Part 1 (40 pts) Ten multiple choice questions, 4 points each

1. Four of the five following statements about the cones in our retina are false. Which one is true?

a) They are more important than the rods for precise vision, such as threading a needle.

b) More cones are attached (pooled) to a single optic nerve cell than are rods.

c) They are more important than the rods for night vision.

d) They can never change their sensitivy to light.

e) They are most numerous outside of the fovea.

2. Most of the bending (refraction) of light rays which enter our eyes is done by the

a) The aqueous and vitreous humors.

b) The eyelens.

c) The cornea.

d) The sclera.

e) The retina.

3. The curve shows the intensity distribution of a light bulb. What do we perceive the color to be?

a) Saturated reddish blue

b) Red

c) Unsaturated magenta

d) Unsaturated blue

e) Unsaturated green

4. Four out of the following five statements about accommodation of your eyelens are true. Which one is false?

a) Accommodation is the same thing as changing the bulge of the eyelens.

b) A normal eye can accommodate from zero to 4 Diopters

c) Accommodation allows you to eventually see in a dark movie theater when you come in from the light

d) Accommodation is the same thing as changing the focal length of the eyelens.

e) Hyperopic and myopic people can have normal accommodation.

5. What is the focal length of a 100 diameter lens set at f-stop f/4?

a) 40 mm, b) 100 mm, c) 200 mm, d) 400 mm, e) 800 mm

6. What is the f-number needed to get the same exposure when the aperture diameter is reduced to 50 mm?

a) f/8, b) f/5.6, c) f/4, d) f/2.8, e) f/2 (not well-posed problem everyone gets full credit)

7. In order to get the greatest depth of field which f/stop should you use

a) f/2, b) f/2.8, c) f/4, d) f/5.6, e) f/8

8. Consider a set of five f/stops paired with appropriate shutter speeds so that all the f/stop-shutter-speed pairs give the same exposure. Which is the best f/stop (based on the associated shutter speed) to photograph a basketball player in motion?

a) f/2, b) f/2.8, c) f/4, d) f/5.6, e) f/8

9. A brief image is projected on a screen for 0.01 secs. You perceive an afterimage after a delay time shown in the figure. The afterimage lasts for a persistence time, as shown. When should the next image be projected on the screen to give the illusion of smooth motion (a movie)?

a) During the projection interval of the brief image

b) During the delay interval

c) During the persistence time of the after-image

d) After the persistence time of the after-image

10. If the brief image is on the screen for 0.002 secs and the time between brief images is 0.020 secs, for how much of the time is there a real image on the screen while you watch a movie?

a) roughly 1% of the time

b) roughly 10% of the time

c) roughly 5% of the time

d) roughly 50% of the time

e) 100% of the time

Part II (60 pts): Problem solving (answer all parts and show your work)

11) [20 pts]

a) [4] In vision, what is meant by a person's "near point?"

Your near point is the closest distance in front of your eyes that you can put an object (such as a book) and see it clearly. At this distance your eyelens is fully accommodated (bulged). For normal eyes the near point is 25 cm.

b) [6] What is meant by an "intermediate image" when two lenses combined make an image?

The image of an object produced by one lens alone (without the second) is called the "intermediate image." It acts as an effective object for the second lens alone (without the first). The image of that effective object produced by the second lens alone is the same as the image produced by the two lenses combined.

c) [10] Elizabeth has a near point of 40 cm without glasses. At the drugstore she finds reading glasses labeled 1.25 D, 1.5 D, 1.75 D and 2 D. Which glasses should she buy in order for her to clearly read a book 25 cm from my eyes? Show your work and explain in words.

The lens equation for the reading glasses is 1/f = 1/x₀ + 1/x_i.

Given: x₀ = .25 m is the distance from the glasses to the book. Near point is d = 0.4 m.

We need the reading glasses to have the correct focal length and diopter power to put the (intermediate) image at hr near point. Hence, x_i = -d = -0.4 m (minus sign because the (intermediate) image is on the same side of the glasses as the book (object)).

Plug into the lens eqn. 1/f = 1/0.25 – 1/0.4 = 4 – 2.5 = 1.5.

Since the distances are all in meters the necessary power of the glasses P = 1/f is diopters (signified by the symbol, D). Hence, she should choose the 1.5 D reading glasses.

12) [20 pts]

a) (4) What is meant by "lightness constancy"?

Lightness constancy means that when looking at a picture, a person's face or a landscape or anything else, we perceive relatively darker or lighter adjacent regions of the image more than we perceive the overall light level. For example, a picture looks the same whether we view it in bright light or in the shade.

b) (6) At left is a sketch of a "receptive field" in your retina. Explain what it is and what happens when different parts of it are exposed to light parts of an image on your retina.

A receptive field is a group of rods or cones which convey information about the lightness or darkness of parts of an image on your retina. All of the rods or cones from a single receptive field send their signal through intermediate neural cells to a single ganglion neural cell in your retina which then forwards a signal to the brain about whether the receptive field is centered in a dark or light region of the image. The receptive field consists of a central disk and an annular surround. Image light falling on the center increases the ambient signal from that ganglion cell to the brain, suggesting a light region. Image light falling on the surround decreases the ambient signal from that ganglion cell to the brain suggesting a dark region. The ganglion cell averages the suggestions from the center and from the surround when determining what message to send to the brain. The receptive field is designed so that equal light falling on the center and surround does not change the ambient signal to the brain. Hence, we are much more sensitive to boundaries between light and dark regions of the image on our retina than we are to the overall level of light. This is why we perceive lightness constancy of an object.

c) (10) In the checkerboard at left, the squares labeled A and B seem to be of different lightnesses even though they are not. Explain this in words and by drawing receptive fields in appropriate places on appropriate squares.

The receptive field shown on square A sends the message dark to its ganglion cell and your brain because of signal suppression due to light falling on part of its surround. The receptive field shown on square B sends the message light to to the brain because part of its surround is in the dark and therefore does not inhibit the signal. The influence of the adjacent squares influences our perception of the lightness or darkness of squares A and B. They are actually of exactly the same lightness relative to each other!!

13) [20 pts] In the chromaticity diagram the point W is white and the spectral colors are around the horseshoe, labeled by their wavelength in nm.

a) (4) What is the dominant hue of the color marked by P? Explain how you get the dominant hue.

Draw a line from white through P. It will intersect the rim of the horseshoe at the wavelength 500 nm, which is the dominant hue, which is wavelength green or wavelength cyan.

b) (2) Is the color P a saturated or unsaturated color?

It is an unsaturated color since it is not on the rim of the chromaticity diagram.

c) (6) Show on the chromaticity diagram the gamut of colors that can be reproduced by additively mixing three colors: pure white (the color labeled W) and the spectral colors 500 nm and 480 nm. Name the colors in words (see front page of exam) and indicate whether they are saturated or unsaturated.

The colors which can be produced by additive mixing are all of the colors inside the triangle between W, 500 nm and 480 nm. In addition to the two wavelength colors you can make unsaturated greens, cyan and light blue, as well as off-whites with blue or green tints in them.

d) (4) What other wavelength colors besides 500 nm and 480 nm can you reproduce by additively mixing those three colors?

None, because there are no wavelength colors inside the triangle.

e) (4) Explain how you could partitively mix the above three colors.

You could partitively mix by putting white, green and blue dots close to each other, although you will find it hard to make spectral green or blue dots.