# How did they come to the conclusion of 2/3h? Thanks! How did they come to the...

###### Question:

How did they come to the conclusion of 2/3h? Thanks!

How did they come to the conclusion of 2/3h? Can someone show me exactly how they got to this number?
EXAMPLE 26-1 REFLECTING ON A FLOWER to the leit ofa An observer is at table level, a distance d to the left of a flower of height h. The flower itself is a distance d to as shown in the sketch. Note that a ray of light propagating from the top of the flower to the observer's eye refet. ror at a height y above the table. Find y in terms of the height of the flower, h. PICTURE THE PROBLEM The physical situation is shown in the diagram, along with a ray from the top of the flower to the eye of the observer. The point where the ray hits the mirror is a height y above the table. The flower is a distance d to the left of the mirror and its image is a distance d to the right of the mirror. Finally, the observer's eye is a distance 2d to the left of the mirror STRATEGY To find y, we must use the fact that the angle of reflection is equal to the angle follows, then, that tan 0 obtained from the small yellow triangle must be equal tan 0 equal to one another yields a relation that can be solved for y. of incidence. In the diagram we indicate these two angles by the symbol 6. It to tan 0 obtained from the larger green triangle. Setting these expressions for
26-2 FORMING IMAGES WITH A PLANE MIRROR 911 SOLUTION 1 Wit an expression for tan e tusing the yelow triangle h- y Now, write a similar expression for tan θ using the green triangle 2 3. Set the two expressions for tan 6 equal to one another: L Rearrange the preceding equation and solve for y: 2d d 2d h-y- INSIGHT Netethat the observer will see the entire image of the flower in a section of mirror that is only two-thirds the height of the flower. RACTICE PROBLEM l the observer moves farther from the base nd ocation? As a check on your answer, calculate the point of reflection for th r from the base of the flower, does the point of reflection move upward, downward, or stay at the e case where the distance between the observer the base of the flower is 2d. (Answer The point of reflection moves upward. In this case, we find y- on nlaled homework problems Problen 5,Problem 7

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The text passage provided contains a question about a mathematical derivation, specifically about how a value of \( \frac{2}{3}h \) was obtained in a physics problem. The question is repeated, indicating a strong focus on understanding this particular calculation. The passage also includes a detailed example problem and solution related to the reflection of light and the height of an image formed by a plane mirror.
single_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# How did they come to the conclusion of 2/3h? Thanks! How did they come to the...

###### Question:

How did they come to the conclusion of 2/3h? Thanks!

How did they come to the conclusion of 2/3h? Can someone show me exactly how they got to this number?
EXAMPLE 26-1 REFLECTING ON A FLOWER to the leit ofa An observer is at table level, a distance d to the left of a flower of height h. The flower itself is a distance d to as shown in the sketch. Note that a ray of light propagating from the top of the flower to the observer's eye refet. ror at a height y above the table. Find y in terms of the height of the flower, h. PICTURE THE PROBLEM The physical situation is shown in the diagram, along with a ray from the top of the flower to the eye of the observer. The point where the ray hits the mirror is a height y above the table. The flower is a distance d to the left of the mirror and its image is a distance d to the right of the mirror. Finally, the observer's eye is a distance 2d to the left of the mirror STRATEGY To find y, we must use the fact that the angle of reflection is equal to the angle follows, then, that tan 0 obtained from the small yellow triangle must be equal tan 0 equal to one another yields a relation that can be solved for y. of incidence. In the diagram we indicate these two angles by the symbol 6. It to tan 0 obtained from the larger green triangle. Setting these expressions for
26-2 FORMING IMAGES WITH A PLANE MIRROR 911 SOLUTION 1 Wit an expression for tan e tusing the yelow triangle h- y Now, write a similar expression for tan θ using the green triangle 2 3. Set the two expressions for tan 6 equal to one another: L Rearrange the preceding equation and solve for y: 2d d 2d h-y- INSIGHT Netethat the observer will see the entire image of the flower in a section of mirror that is only two-thirds the height of the flower. RACTICE PROBLEM l the observer moves farther from the base nd ocation? As a check on your answer, calculate the point of reflection for th r from the base of the flower, does the point of reflection move upward, downward, or stay at the e case where the distance between the observer the base of the flower is 2d. (Answer The point of reflection moves upward. In this case, we find y- on nlaled homework problems Problen 5,Problem 7

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user
The text passage provided contains a question about a mathematical derivation, specifically about how a value of \( \frac{2}{3}h \) was obtained in a physics problem. The question is repeated, indicating a strong focus on understanding this particular calculation. The passage also includes a detailed example problem and solution related to the reflection of light and the height of an image formed by a plane mirror.

TYPE: SINGLE_QUESTION