To calculate the height of the image formed by the convex mirror, we can use the mirror equation:
1/f = 1/v + 1/u
Where:
- f is the focal length of the mirror,
- v is the distance of the image from the mirror (which is what we want to find),
- u is the distance of the object from the mirror.
Using the given values:
f = 10cm
u = 20cm
Plugging these values into the equation:
1/10 = 1/v + 1/20
To simplify the equation, we can find the common denominator:
1/10 = (2 + 1)/v
Multiplying both sides by 10v to eliminate the fractions:
v = 3v + 15
Subtracting 3v from both sides:
-2v = 15
Dividing both sides by -2:
v = -15/2
Since the image is formed on the opposite side of the mirror, the distance is negative. However, in this case, we are only interested in the magnitude of the distance, so we take the absolute value:
|v| = |-15/2| = 15/2
So, the distance of the image from the mirror is 15/2 cm.
To calculate the height of the image, we can use the magnification formula:
magnification = -v/u
Plugging in the values:
magnification = -(15/2) / 20 = -15/40 = -3/8
The negative sign indicates that the image is inverted.
Now, we can calculate the height of the image. The magnification formula states that the height of the image is equal to the magnification multiplied by the height of the object.
Using the given value:
height of object = 2.5cm
Height of image = (-3/8) * 2.5 = -7.5/8 = -15/16
Again, the negative sign indicates that the image is inverted.
Therefore, the height of the image formed by the convex mirror is -15/16 cm.
An object of height 2•5cm is placed at 20cm from a convex mirror of focal length 10cm. Calculate the height of the image formed.
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