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A: If you are 5.5 feet tall, how tall a mirror do you need to see yourself head ...

Sep 15, 2024

A: If you are 5.5 feet tall, how tall a mirror do you need to see yourself head to toe? Where on the wall should the mirror be mounted? Use the "A" drawing to show your answers graphically. If you are standing in position 1 or in position 2, does the size of the mirror necessary to reflect your image change? Circle the correct YES or NO answer in the drawing. B: in the "B" drawing, the static object is the green person standing 1 meter from the mirror and the observer is the red person, who moves around. Draw the virtual image of the object including position and orientation. Would the image of the object appear to be in a different position to the observer as they move around? Circle the correct YES or NO answer in the drawing. C: In the "C" drawing, you are the blue person with red arms. You are seen from above, as you stand in front of a mirror. Your left arm points to your left, your right arm points to the mirror, as represented by red arrows. Draw the virtual image of you including position and orientation. Does the mirror flip left to right? Does the mirror flip front to back? (Hint: look at your left arm and its image, then at the right arm and its image, respectively, to answer the latter two questions.) Circle the correct YES or NO answers in the drawing.

Solution

To see your full height in the mirror, the mirror should be at least half your height. Therefore, if you are 5.5 feet tall, the minimum height of the mirror required is

\frac{5.5}{2} = 2.75 \text{ feet}

. The mirror should be mounted so that the top of the mirror is at your eye level, which is typically around 5.5 feet. Thus, the bottom of the mirror should be approximately 2.75 feet from the ground. The size of the mirror does not change when you move from position 1 to position 2, so the answer is NO

The virtual image of the green object will appear to be 1 meter behind the mirror. As the red observer moves around, the image will remain in the same position relative to the mirror, so the observer will see the image in the same position regardless of their movement. Therefore, the answer is NO

The mirror does not flip the image left to right; it flips it front to back. When you raise your left arm, the image in the mirror will show the right arm raised, indicating that the mirror flips front to back. Thus, the answer to "Does the mirror flip left to right?" is NO, and for "Does the mirror flip front to back?" the answer is YES

Answer

a: NO, b: NO, c: Left to right: NO, Front to back: YES

Key Concept

Reflection in mirrors: The size of the mirror needed to see a full image is half the height of the object. The virtual image created by a mirror is located behind the mirror at the same distance as the object in front. Mirrors do not flip images left to right; they flip them front to back.

Explanation

The answers are derived from the principles of reflection and the geometry of mirrors, which dictate how images are formed and perceived. The height of the mirror and the nature of the image are consistent regardless of the observer's position.