An object is placed 12cm form a concave mirror which forms its real image at a
distance of 18cm. calculate the focal length of the mirror.
Answers
u= object distance (always negative)
v= image distance (positive)
f =focal lenght (always negative)
answer is --36cm focal length
The focal length of the concave mirror is -12cm.
Given:
An object is placed 12cm form a concave mirror which forms its real image at a distance of 18cm.
To Find:
calculate the focal length of the mirror.
Solution:
To calculate the focal length of a concave mirror when the object distance and image distance are known, we can use the mirror formula:
1/f = 1/do + 1/di
where:
f = focal length of the mirror
do = object distance from the mirror
di = image distance from the mirror
In this case, the object is placed 12cm from the concave mirror and the real image is formed at a distance of 18cm, so we have:
do = -12cm (negative sign indicates that the object is in front of the mirror)
di = -18cm (negative sign indicates that the image is formed on the opposite side of the mirror)
Substituting these values in the mirror formula, we get:
1/f = 1/-12 + 1/-18
Simplifying this expression, we get:
1/f = -3/36
Multiplying both sides by 36, we get:
36/f = -3
Dividing both sides by -3, we get:
f = -12cm
Therefore, the focal length of the concave mirror is -12cm. Note that the negative sign indicates that the mirror is a concave mirror, as opposed to a convex mirror, which has a positive focal length.
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