Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is:40 cm
Question
Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is:40 cm
Solution
To solve this problem, we first need to understand the mirror formula and the magnification formula.
The mirror formula is 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.
The magnification formula is m = -v/u.
Given that the radius of curvature is 40 cm, we know that the focal length (f) is half of this, so f = 20 cm.
- For object A:
We can substitute the values into the mirror formula: 1/20 = 1/v + 1/-15
Solving for v (the image distance), we get v = -60 cm. This means the image is formed 60 cm in front of the mirror.
- For object B:
Again, we substitute the values into the mirror formula: 1/20 = 1/v + 1/-25
Solving for v, we get v = -40 cm. This means the image is formed 40 cm in front of the mirror.
- To find the distance between the two images:
We subtract the smaller distance from the larger one: -60 cm - (-40 cm) = -20 cm.
Therefore, the distance between the two images is 20 cm.
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