An object of heights 5 cm is placed at 20 cm from a concave mirror of focal length 10 cm. the image height is?

Answer Details

The problem involves a concave mirror and an object placed in front of it. We are given that the object height is 5 cm, and the object is placed at a distance of 20 cm from the mirror, which has a focal length of 10 cm.
To find the image height, we can use the mirror formula:
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, and u is the distance of the object from the mirror.
We can rearrange the formula to solve for v:
1/v = 1/f - 1/u
Substituting the given values, we get:
1/v = 1/10 - 1/20
Simplifying:
1/v = 1/20
v = 20 cm
This means that the image is formed at a distance of 20 cm behind the mirror.
Now, we can use the magnification formula:
m = -v/u
where m is the magnification of the image.
Substituting the given values, we get:
m = -20/20 = -1
The negative sign indicates that the image is inverted.
Finally, we can use the formula for image height:
hi = -m * ho
where hi is the height of the image, and ho is the height of the object.
Substituting the given values, we get:
hi = -(-1) * 5 = 5 cm
Therefore, the image height is 5 cm, which is the same as the height of the object.
So, the correct answer is: 5 cm.