1. Consider a diffraction grating, marked at 100 lines (slits) per mm. A 632nm laser hits it. A screen is 0.75-m away from the grating. Find the following:
a. the distance between slits (in mm)
b. the distance between slits (in m)
c. the diffraction angle for n=1
d. the distance between n=0 and n=1 on the wall (which is 0.75-m away)
e. the highest order (n) that you can get from this grating and laser combination
2. Repeat the above problem for a 450nm laser.
3. Explain superposition of waves.
4. Explain diffraction.
5. Two identical charges are 0.25-m apart. If the force between them is 25-N, what is the magnitude of each charge? Is this force attractive or repulsive? Can you tell the sign of the charges?
6. Consider a 100 uC (10^-6) charge, 0.01-m away from a -300 uC charge. Find the following:
a. the force between them
b. whether or not this force is attractive or repulsive
c. the new force, if the distance is doubled
d. draw the electric field between the charges
In preparation for next class:
7. Define voltage (electric potential), current, resistance and power. Also, give the units for each.
8. What is Ohm's Law?
9. If a 9-V battery is in series with a 25-ohm resistor, what current is drawn from the battery? How much charge "flows" during one minute? What is the power radiated (in heat) by the resistor?
Thursday, July 28, 2011
Wednesday, July 27, 2011
Monday, July 25, 2011
Interference and Diffraction
http://www.falstad.com/ripple/index.html
This is the "ripple tank" applet I showed in class. Play around with 2-source interference and note locations of constructive and destructive interference. This also happens with light waves.
The mathematical relationship:
n lambda = d sin(theta)
n is the "image order number," going from 0 (central image, directly in line with the light source) to n=1 (first order image, the same on either side of the central image), to n=2, etc.
lambda is the wavelength of light
d is the distance of separation between "slits"
theta is the angle of diffraction
This is the "ripple tank" applet I showed in class. Play around with 2-source interference and note locations of constructive and destructive interference. This also happens with light waves.
The mathematical relationship:
n lambda = d sin(theta)
n is the "image order number," going from 0 (central image, directly in line with the light source) to n=1 (first order image, the same on either side of the central image), to n=2, etc.
lambda is the wavelength of light
d is the distance of separation between "slits"
theta is the angle of diffraction
Lens and Mirror problems
1. Compare and contrast convex and concave lenses.
2. Compare and contrast convex and concave mirrors.
3. Consider a lens, f = +12cm, with an object located 20cm in front of it. Find the following:
a. type of lens
b. di
c. type of image (real or virtual)
d. magnification of image
e. whether or not image is upside-down or right-side up
f. Where could you place object so that you get NO image?
g. Where could you place object so that you only get virtual images?
4. Repeat question 3 for a lens with f = -12cm.
5. Repeat question 3 for a mirror with f = +20cm.
6. Give a practical use for a convex lens, concave lens, convex mirror and concave mirror. (One for each.)
7. What is, in general, the effect of covering a lens or mirror in half?
2. Compare and contrast convex and concave mirrors.
3. Consider a lens, f = +12cm, with an object located 20cm in front of it. Find the following:
a. type of lens
b. di
c. type of image (real or virtual)
d. magnification of image
e. whether or not image is upside-down or right-side up
f. Where could you place object so that you get NO image?
g. Where could you place object so that you only get virtual images?
4. Repeat question 3 for a lens with f = -12cm.
5. Repeat question 3 for a mirror with f = +20cm.
6. Give a practical use for a convex lens, concave lens, convex mirror and concave mirror. (One for each.)
7. What is, in general, the effect of covering a lens or mirror in half?
Lens / Mirror Applet
http://www.phys.hawaii.edu/~teb/java/ntnujava/Lens/lens_e.html
Recall:
Lenses:
+f, convex lens (can form both real and virtual images, depending on do)
-f, concave lens (forms ONLY virtual images, since light rays always diverge)
Mirrors
+f, concave mirror (can form both real and virtual images, depending on do)
-f, convex mirror (forms ONLY virtual images, since light rays always diverge)
1/f = 1/di + 1/do
f = (theoretical) focal length
di = image distance (where image forms)
do = object distance (where object is located, relative to lens or mirror)
-di indicates a virtual image
+di indicates a real image
mag = -di/do
-mag indicates upside-down image
+mag indicates right-side up image
If absolute value of mag is > 1, image is larger than object.
If absolute value of mag is < 1, image is smaller than object.
Recall:
Lenses:
+f, convex lens (can form both real and virtual images, depending on do)
-f, concave lens (forms ONLY virtual images, since light rays always diverge)
Mirrors
+f, concave mirror (can form both real and virtual images, depending on do)
-f, convex mirror (forms ONLY virtual images, since light rays always diverge)
1/f = 1/di + 1/do
f = (theoretical) focal length
di = image distance (where image forms)
do = object distance (where object is located, relative to lens or mirror)
-di indicates a virtual image
+di indicates a real image
mag = -di/do
-mag indicates upside-down image
+mag indicates right-side up image
If absolute value of mag is > 1, image is larger than object.
If absolute value of mag is < 1, image is smaller than object.
Tuesday, July 19, 2011
Reflection and Refraction
REFLECTION
You may recall from class the simple, elegant Law of Reflection:
angle of incidence equals angle of reflection.
Think about pool balls hitting the side of a billiards table - angle in equals angle out.
The only tricky part is the way we measure angles - they are measured with respect to a "normal line", a line that is perpendicular to the surface where they hit.
REFRACTION
Refraction refers to a wave changing mediums - going from air to glass, air to water, water to air, glass to air, etc. We first begin by defining a new quantity, the index of refraction (n):
n = c/v
where c is the speed of light and v is the speed of light in the NEW medium. Indices of refraction are always greater than (or approximately equal to) one, and have NO units.
For example, if a substance (say, glass) slows down light to 2/3 of the speed of light (in a vacuum), its index is:
n = c/(2/3 c) = 1.5
A convenient relationship can be derived that relates the angle of incidence and the angle of refraction, along with the indices of refraction of the two mediums. It is called Snell's Law:
n1 sin(theta 1) = n2 sin(theta 2)
As before, the angles are measured with respect to a normal (perpendicular) line. It may be helpful to remember:
- When light goes from a lower density medium (n1) to a higher density medium (n2 > n1), the light ray is refracted TOWARD the normal line. And vice versa.
CRITICAL ANGLE
There is an angle, above which light can not leave the medium. Imagine a light ray trying to go from water into air. Clearly, the light ray will refract AWAY from the normal line. If you gradually increase the angle of incidence (theta 1), eventually the refracted angle (theta 2) will become 90 degrees - light "skating" across the surface.
Any theta 1 greater than this angle will result in "total internal reflection", wherein the light simply cannot leave the substance - it is reflected back inside the original medium. This is the secret of fiber optics. The mathematics come from Snell's Law:
n1 sin(theta 1) = n2 sin(90)
n1 sin(critical angle, ic) = 1 (1)
sin ic = 1/n
That is, the sine of the critical angle equals 1 over the index of refraction for that particular medium (assuming that medium 2 is air, so that n2 = 1).
Got it? Good!
You may recall from class the simple, elegant Law of Reflection:
angle of incidence equals angle of reflection.
Think about pool balls hitting the side of a billiards table - angle in equals angle out.
The only tricky part is the way we measure angles - they are measured with respect to a "normal line", a line that is perpendicular to the surface where they hit.
REFRACTION
Refraction refers to a wave changing mediums - going from air to glass, air to water, water to air, glass to air, etc. We first begin by defining a new quantity, the index of refraction (n):
n = c/v
where c is the speed of light and v is the speed of light in the NEW medium. Indices of refraction are always greater than (or approximately equal to) one, and have NO units.
For example, if a substance (say, glass) slows down light to 2/3 of the speed of light (in a vacuum), its index is:
n = c/(2/3 c) = 1.5
A convenient relationship can be derived that relates the angle of incidence and the angle of refraction, along with the indices of refraction of the two mediums. It is called Snell's Law:
n1 sin(theta 1) = n2 sin(theta 2)
As before, the angles are measured with respect to a normal (perpendicular) line. It may be helpful to remember:
- When light goes from a lower density medium (n1) to a higher density medium (n2 > n1), the light ray is refracted TOWARD the normal line. And vice versa.
CRITICAL ANGLE
There is an angle, above which light can not leave the medium. Imagine a light ray trying to go from water into air. Clearly, the light ray will refract AWAY from the normal line. If you gradually increase the angle of incidence (theta 1), eventually the refracted angle (theta 2) will become 90 degrees - light "skating" across the surface.
Any theta 1 greater than this angle will result in "total internal reflection", wherein the light simply cannot leave the substance - it is reflected back inside the original medium. This is the secret of fiber optics. The mathematics come from Snell's Law:
n1 sin(theta 1) = n2 sin(90)
n1 sin(critical angle, ic) = 1 (1)
sin ic = 1/n
That is, the sine of the critical angle equals 1 over the index of refraction for that particular medium (assuming that medium 2 is air, so that n2 = 1).
Got it? Good!
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