When an object of height 1 cm is kept at a distance 4 cm from a concave mirror, its erect image of height 1.5 cm is formed at a distance 6 cm behind the mirror. Find the focal length of mirror, by draw
Question
When an object of height 1 cm is kept at a distance 4 cm from a concave mirror, its erect image of height 1.5 cm is formed at a distance 6 cm behind the mirror. Find the focal length of mirror, by draw
Solution
To find the focal length of the mirror, we can use 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 -v/u = h'/h, where h' is the height of the image and h is the height of the object.
Given in the problem, u = -4 cm (the negative sign indicates that the object is on the same side as the light being reflected), v = -6 cm (the negative sign indicates that the image is formed on the same side as the light being reflected), h = 1 cm, and h' = -1.5 cm (the negative sign indicates that the image is inverted).
First, let's use the magnification formula to verify the given values:
-v/u = h'/h -(-6)/-4 = -1.5/1 1.5 = 1.5
The given values are correct.
Now, let's use the mirror formula to find the focal length:
1/f = 1/v - 1/u 1/f = 1/-6 - 1/-4 1/f = -1/6 + 1/4 1/f = -4/24 + 6/24 1/f = 2/24 f = 24/2 f = -12 cm
The negative sign indicates that the mirror is a concave mirror. So, the focal length of the mirror is 12 cm.
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