# Talk:QB/d Bell.polarization

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## QB/d_Bell.polarization

### 1

• The light is linearly polarized, the electric field is oriented ________to the direction of motion

- parallel + perpendicular - at 45 degrees - all of these are possible

Electromagnetic radiation makes a so-called transverse wave

### 2

• Hold a pendulum a moderate distance from equilibrium and release it by tossing it in a direction perpendicular to the displacement of the mass from equilibrium. The resulting polarization will be ____ (pick the best answer)

- linearly - circular - circular or linear + circular or elliptical - linear or elliptical

We will do a lab on this. It will be circular only if you carefully select the initial speed. See also q15 below for a complementary question.

### 3

• A mathematically pure (strictly monochromatic) __________ wave (oscillation) that is unpolarized cannot be created

- electromagnetic - pendulum + electromagnetic or pendulum - both can be created

This is a tricky question (click link to see why).

### 4

• To create an unpolarized pendulum oscillation

- create an elliptically polarized wave with an ε>0.2 - create an elliptically polarized wave with an ε<0.8 - create an elliptically polarized wave with an 0.2<ε<0.8 + start with a linear, circular, or elliptical wave and slowly evolve to different polarizations

Another tricky question

### 5

• If the hypotenuse of a 45°-45° right triangle has a length of ${\displaystyle {\sqrt {2}}}$  what is the length of each side?

- ${\displaystyle {\tfrac {1}{2}}}$  - ${\displaystyle {\tfrac {1}{\sqrt {2}}}}$  - ${\displaystyle 1}$  + ${\displaystyle {\sqrt {2}}}$  - ${\displaystyle 2{\sqrt {2}}}$

See subpage at components This is a ${\displaystyle 1:1:{\sqrt {2}}}$  right triangle.

### 6

• If the hypotenuse of a 45°-45° right triangle has a length of ${\displaystyle 1}$  what is the length of each side?

- ${\displaystyle {\tfrac {1}{2}}}$  + ${\displaystyle {\tfrac {1}{\sqrt {2}}}}$  - ${\displaystyle 1}$  - ${\displaystyle {\sqrt {2}}}$  - ${\displaystyle 2{\sqrt {2}}}$

See subpage at components Divide the three lengths of the previous question by ${\displaystyle {\sqrt {2}}}$

### 7

• If the hypotenuse of a 60°-30° right triangle has a length of 1 what is the length of the shorter side?

- ${\displaystyle {\tfrac {1}{4}}}$  - ${\displaystyle {\tfrac {1}{\sqrt {2}}}}$  + ${\displaystyle {\tfrac {1}{2}}}$  - ${\displaystyle {\tfrac {\sqrt {3}}{2}}}$  - ${\displaystyle {\tfrac {3}{4}}}$

See subpage at components ${\displaystyle (1/2)-{\sqrt {3}}/2-1}$  triangle

### 8

• If the hypotenuse of a 60°-30° right triangle has a length of 1 what is the length of the longer side?

- ${\displaystyle {\tfrac {1}{4}}}$  - ${\displaystyle {\tfrac {1}{\sqrt {2}}}}$  - ${\displaystyle {\tfrac {1}{2}}}$  + ${\displaystyle {\tfrac {\sqrt {3}}{2}}}$  - ${\displaystyle {\tfrac {3}{4}}}$

See subpage at components ${\displaystyle (1/2)-{\sqrt {3}}/2-1}$  triangle

### 9

• A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field. By what factor does a filter reduce the electric field if it is oriented 30° to that field?

- ${\displaystyle {\tfrac {1}{4}}}$  - ${\displaystyle {\tfrac {1}{\sqrt {2}}}}$  - ${\displaystyle {\tfrac {1}{2}}}$  + ${\displaystyle {\tfrac {\sqrt {3}}{2}}}$  - ${\displaystyle {\tfrac {3}{4}}}$

See subpage at components. Note that the components of a unit vector at (30°,45°,60°) are ${\displaystyle {\sqrt {3}}/2,1{\sqrt {2}},1/2)}$  which square to ${\displaystyle (3/4,1/2,1/4)}$ . Here we use ${\displaystyle {\sqrt {3}}/2}$

### 10

• A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field. By what factor does a filter reduce the electric field if it is oriented 60° to that field?

- ${\displaystyle {\tfrac {1}{4}}}$  - ${\displaystyle {\tfrac {1}{\sqrt {2}}}}$  + ${\displaystyle {\tfrac {1}{2}}}$  - ${\displaystyle {\tfrac {\sqrt {3}}{2}}}$  - ${\displaystyle {\tfrac {3}{4}}}$

See subpage at components. Note that the components of a unit vector at (30°,45°,60°) are ${\displaystyle {\sqrt {3}}/2,1{\sqrt {2}},1/2)}$  which square to ${\displaystyle (3/4,1/2,1/4)}$ . Here we use ${\displaystyle 1/2}$

### 11

• A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field. A 12 mW laser strikes a polarizing filter oriented 30° to the incoming axis of polarization. How much power passes the filter?

- 3mW - 4mW - 6mW - 8mW + 9mW

See subpage at components. Note that the components of a unit vector at (30°,45°,60°) are ${\displaystyle {\sqrt {3}}/2,1{\sqrt {2}},1/2)}$  which square to ${\displaystyle (3/4,1/2,1/4)}$ . Here we use ${\displaystyle (3/4)(12)=9}$

### 12

• A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field.A 12 mW laser strikes a polarizing filter oriented 30° to the incoming axis of polarization. How much power is blocked by the filter?

+ 3mW - 4mW - 6mW - 8mW - 9mW

### 13

• A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field.A 12 mW laser strikes a polarizing filter oriented 60° to the incoming axis of polarization. How much power is blocked by the filter?

- 3mW - 4mW - 6mW - 8mW + 9mW

### 14

• A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field.A 12 mW laser strikes a polarizing filter oriented 60° to the incoming axis of polarization. How much power is passed by the filter?

+ 3mW - 4mW - 6mW - 8mW - 9mW

### 15

• A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field.A 12 mW laser strikes a polarizing filter oriented 45° to the incoming axis of polarization. How much power is passed by the filter?

- 3mW - 4mW + 6mW - 8mW - 9mW

### 16

• A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field. Unpolarized light impinges on three linear filters, each oriented 45° to the previous, as shown. What fraction of the power incident on the first filter emerges from the last?

- 1/32 - 1/16 - 3/32 + 1/8 - 3/16

See subpage at components. The hardest one. The first filter blocks half, as do the second and third filters. With three filters, each blocking half, we have: (1/2)(1/2)(1/2)=1/8.

### 17

• Hold a pendulum a moderate distance from equilibrium and release it by tossing it in a direction parallel to the displacement of the mass from equilibrium. The resulting polarization will be ____ (pick the best answer)

+ linearly - circular - circular or linear - circular or elliptical - linear or elliptical

See q2 above. This is perhaps a trick question and should be discussed in lecture if it will appear on any of the exams associated with a given course.

### 18

• A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field. Unpolarized light impinges on three linear filters. The second is oriented 30° from the first, and the third is rotated by an additional 60°, making it at right angles from the first filter. What fraction of the power incident on the first filter emerges from the last?

- 1/32 - 1/16 + 3/32 - 1/8 - 3/16

See subpage at components. The hardest one. The first filter blocks half, as do the second and third filters. The first passes 1/2, the second passes 3/4 of that, and the final passes 1/4 of what's left. The net amount passed is (1/2)(3/4)(1/4)=3/32

## Raw script

t QB/d_Bell.polarization
! q1 CCO (public domain) user:Guy vandegrift
? The light is linearly polarized, the electric field is oriented ________to the direction of motion
- parallel
+ perpendicular
- at 45 degrees
- all of these are possible
$Electromagnetic radiation makes a so-called transverse wave ! q2 CCO (public domain) user:Guy vandegrift ? Hold a pendulum a moderate distance from equilibrium and release it by tossing it in a direction perpendicular to the displacement of the mass from equilibrium. The resulting polarization will be ____ (pick the best answer) - linearly - circular - circular or linear + circular or elliptical - linear or elliptical$ We will do a lab on this. It will be circular only if you carefully select the initial speed. See also q15 below for a complementary question.

! q3 CCO (public domain) user:Guy vandegrift
? A mathematically pure (strictly monochromatic) __________ wave (oscillation) that is unpolarized cannot be created
- electromagnetic
- pendulum
+ electromagnetic or pendulum
- both can be created
$This is a tricky question (click link to see why). ! q4 CCO (public domain) user:Guy vandegrift ? To create an unpolarized pendulum oscillation - create an elliptically polarized wave with an ε>0.2 - create an elliptically polarized wave with an ε<0.8 - create an elliptically polarized wave with an 0.2<ε<0.8 + start with a linear, circular, or elliptical wave and slowly evolve to different polarizations$ Another tricky question

! q5 CCO (public domain) user:Guy vandegrift
?If the hypotenuse of a 45°-45° right triangle has a length of ${\displaystyle {\sqrt {2}}}$  what is the length of each side?
- ${\displaystyle {\tfrac {1}{2}}}$
- ${\displaystyle {\tfrac {1}{\sqrt {2}}}}$
- ${\displaystyle 1}$
+ ${\displaystyle {\sqrt {2}}}$
- ${\displaystyle 2{\sqrt {2}}}$
$See subpage at components This is a ${\displaystyle 1:1:{\sqrt {2}}}$ right triangle. ! q6 CCO (public domain) user:Guy vandegrift ?If the hypotenuse of a 45°-45° right triangle has a length of ${\displaystyle 1}$ what is the length of each side? - ${\displaystyle {\tfrac {1}{2}}}$ + ${\displaystyle {\tfrac {1}{\sqrt {2}}}}$ - ${\displaystyle 1}$ - ${\displaystyle {\sqrt {2}}}$ - ${\displaystyle 2{\sqrt {2}}}$$ See subpage at components Divide the three lengths of the previous question by ${\displaystyle {\sqrt {2}}}$

! q7 CCO (public domain) user:Guy vandegrift
?If the hypotenuse of a 60°-30° right triangle has a length of 1 what is the length of the shorter side?
- ${\displaystyle {\tfrac {1}{4}}}$
- ${\displaystyle {\tfrac {1}{\sqrt {2}}}}$
+ ${\displaystyle {\tfrac {1}{2}}}$
- ${\displaystyle {\tfrac {\sqrt {3}}{2}}}$
- ${\displaystyle {\tfrac {3}{4}}}$
$See subpage at components ${\displaystyle (1/2)-{\sqrt {3}}/2-1}$ triangle ! q8 CCO (public domain) user:Guy vandegrift ?If the hypotenuse of a 60°-30° right triangle has a length of 1 what is the length of the longer side? - ${\displaystyle {\tfrac {1}{4}}}$ - ${\displaystyle {\tfrac {1}{\sqrt {2}}}}$ - ${\displaystyle {\tfrac {1}{2}}}$ + ${\displaystyle {\tfrac {\sqrt {3}}{2}}}$ - ${\displaystyle {\tfrac {3}{4}}}$$ See subpage at components ${\displaystyle (1/2)-{\sqrt {3}}/2-1}$  triangle

! q9 CCO (public domain) user:Guy vandegrift
? A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field. By what factor does a filter reduce the electric field if it is oriented 30° to that field?
- ${\displaystyle {\tfrac {1}{4}}}$
- ${\displaystyle {\tfrac {1}{\sqrt {2}}}}$
- ${\displaystyle {\tfrac {1}{2}}}$
+ ${\displaystyle {\tfrac {\sqrt {3}}{2}}}$
- ${\displaystyle {\tfrac {3}{4}}}$
$See subpage at components. Note that the components of a unit vector at (30°,45°,60°) are ${\displaystyle {\sqrt {3}}/2,1{\sqrt {2}},1/2)}$ which square to ${\displaystyle (3/4,1/2,1/4)}$ . Here we use ${\displaystyle {\sqrt {3}}/2}$ ! q10 CCO (public domain) user:Guy vandegrift ? A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field. By what factor does a filter reduce the electric field if it is oriented 60° to that field? - ${\displaystyle {\tfrac {1}{4}}}$ - ${\displaystyle {\tfrac {1}{\sqrt {2}}}}$ + ${\displaystyle {\tfrac {1}{2}}}$ - ${\displaystyle {\tfrac {\sqrt {3}}{2}}}$ - ${\displaystyle {\tfrac {3}{4}}}$$ See subpage at components. Note that the components of a unit vector at (30°,45°,60°) are ${\displaystyle {\sqrt {3}}/2,1{\sqrt {2}},1/2)}$  which square to ${\displaystyle (3/4,1/2,1/4)}$ . Here we use ${\displaystyle 1/2}$

! q11 CCO (public domain) user:Guy vandegrift
? A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field. A 12 mW laser strikes a polarizing filter oriented 30° to the incoming axis of polarization. How much power passes the filter?
- 3mW
- 4mW
- 6mW
- 8mW
+ 9mW
$See subpage at components. Note that the components of a unit vector at (30°,45°,60°) are ${\displaystyle {\sqrt {3}}/2,1{\sqrt {2}},1/2)}$ which square to ${\displaystyle (3/4,1/2,1/4)}$ . Here we use ${\displaystyle (3/4)(12)=9}$ ! q12 CCO (public domain) user:Guy vandegrift ? A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field.A 12 mW laser strikes a polarizing filter oriented 30° to the incoming axis of polarization. How much power is blocked by the filter? + 3mW - 4mW - 6mW - 8mW - 9mW$ See subpage at components. Note that the components of a unit vector at (30°,45°,60°) are ${\displaystyle {\sqrt {3}}/2,1{\sqrt {2}},1/2)}$  which square to ${\displaystyle (3/4,1/2,1/4)}$ . Here we use ${\displaystyle (3/4)(12)=9}$  to get the amount blocked. Therefore 12−9=3 is passed.

! q13 CCO (public domain) user:Guy vandegrift
? A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field.A 12 mW laser strikes a polarizing filter oriented 60° to the incoming axis of polarization. How much power is blocked by the filter?
- 3mW
- 4mW
- 6mW
- 8mW
+ 9mW

$See subpage at components. Note that the components of a unit vector at (30°,45°,60°) are ${\displaystyle {\sqrt {3}}/2,1{\sqrt {2}},1/2)}$ which square to ${\displaystyle (3/4,1/2,1/4)}$ . Here, ${\displaystyle (1/4)(12)=3}$ mw is passed so that 9mw is blocked ! q13 CCO (public domain) user:Guy vandegrift ? A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field.A 12 mW laser strikes a polarizing filter oriented 60° to the incoming axis of polarization. How much power is passed by the filter? + 3mW - 4mW - 6mW - 8mW - 9mW$ See subpage at components. Note that the components of a unit vector at (30°,45°,60°) are ${\displaystyle {\sqrt {3}}/2,1{\sqrt {2}},1/2)}$  which square to ${\displaystyle (3/4,1/2,1/4)}$ . Here, ${\displaystyle (1/4)(12)=3}$ mw is passed.

! q14 CCO (public domain) user:Guy vandegrift
? A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field.A 12 mW laser strikes a polarizing filter oriented 45° to the incoming axis of polarization. How much power is passed by the filter?
- 3mW
- 4mW
+ 6mW
- 8mW
- 9mW

$See subpage at components. Note that the components of a unit vector at (30°,45°,60°) are ${\displaystyle {\sqrt {3}}/2,1{\sqrt {2}},1/2)}$ which square to ${\displaystyle (3/4,1/2,1/4)}$ . Here, ${\displaystyle (1/2)(12)=6}$ mw is passed. ! q14 CCO (public domain) user:Guy vandegrift ? A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field. Unpolarized light impinges on three linear filters, each oriented 45° to the previous, as shown. What fraction of the power incident on the first filter emerges from the last? - 1/32 - 1/16 - 3/32 + 1/8 - 3/16$ See subpage at components. The hardest one. The first filter blocks half, as do the second and third filters. With three filters, each blocking half, we have: (1/2)(1/2)(1/2)=1/8.

! q15 CCO (public domain) user:Guy vandegrift
? Hold a pendulum a moderate distance from equilibrium and release it by tossing it in a direction parallel to the displacement of the mass from equilibrium. The resulting polarization will be ____ (pick the best answer)
+ linearly
- circular
- circular or linear
- circular or elliptical
- linear or elliptical
$See q2 above. This is perhaps a trick question and should be discussed in lecture if it will appear on any of the exams associated with a given course. ! q16 CCO (public domain) user:Guy vandegrift ? A linear polarizer selects a component of the electric field. Also, the energy density of light is proportional to the square of the electric field. Unpolarized light impinges on three linear filters. The second is oriented 30° from the first, and the third is rotated by an additional 60°, making it at right angles from the first filter. What fraction of the power incident on the first filter emerges from the last? - 1/32 - 1/16 + 3/32 - 1/8 - 3/16$ See subpage at components. The hardest one. The first filter blocks half, as do the second and third filters. The first passes 1/2, the second passes 3/4 of that, and the final passes 1/4 of what's left. The net amount passed is (1/2)(3/4)(1/4)=3/32
z

### More discussion

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