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