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If the patient is 1.0m from the mirror, where should the lamp be placed relative to the mirror ... One such light has a mirror with a focal length of 20 cm.

User Sourav
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2 Answers

4 votes

Final answer:

The lamp should be placed 33.33 cm in front of the mirror.

Step-by-step explanation:

In order to determine where the lamp should be placed relative to the mirror, we can use the mirror formula:

1/f = 1/do + 1/di

Where f is the focal length of the mirror, and do and di are the object and image distances respectively.

In this case, the focal length of the mirror is given as 20 cm. The object distance, do, is 1.0 m (or 100 cm), and the image distance, di, is unknown.

Plugging in these values, we can solve for di:

1/20 = 1/100 + 1/di

Simplifying, we get:

1/di = 1/20 - 1/100

1/di = 4/100 - 1/100

1/di = 3/100

di = 100/3 cm

Therefore, the image will be located at approximately 33.33 cm from the mirror.

Since the lamp is placed 1.0 m from the mirror, the lamp should be placed 33.33 cm in front of the mirror.

User Soufiene
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5 votes

The ideal placement of the lamp is 0.2 meters in front of the mirror.

How to solve

To determine the ideal placement of the lamp, we can use the mirror formula:

1/f = 1/v + 1/u

where:

f is the focal length of the mirror (0.2 meters in this case)

v is the distance between the image and the mirror (we want to maximize this distance for maximum illumination)

u is the distance between the object and the mirror (1.0 meter in this case)

Plugging in the values, we get:

1/0.2 = 1/v + 1/1

Solving for v, we get:

v = 0.333 meters

This means that the image should be formed 0.333 meters behind the mirror. To ensure that the light rays from the lamp are focused on the patient's face, we need to place the lamp at the focal point of the mirror.

Since the focal length is 0.2 meters, the lamp should be placed 0.2 meters in front of the mirror.

Therefore, the ideal placement of the lamp is 0.2 meters in front of the mirror.

The Complete Question

In a medical examination room, a patient is positioned 1.0 meter away from a mirror. To ensure proper illumination for the examination, a lamp with a mirror attachment, having a focal length of 20 cm, needs to be placed relative to the mirror. Determine the ideal placement of the lamp with respect to the mirror to ensure maximum illumination on the patient's face

User Nocker
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