An object which is 3cm high is placed vertically 10cm in front of a concave mirror. If this object produces an image 40cm from the mirror, the height of the...
An object which is 3cm high is placed vertically 10cm in front of a concave mirror. If this object produces an image 40cm from the mirror, the height of the image is
Answer Details
To solve this problem, 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 are given u = 10cm and v = 40cm. To find f, we can rearrange the formula:
1/f = 1/v + 1/u
1/f = 1/40 + 1/10
1/f = 0.03
f = 33.33cm
Now, we can use the magnification formula:
m = -v/u
where m is the magnification of the image.
Plugging in the values, we get:
m = -v/u
m = -40/10
m = -4
The negative sign indicates that the image is inverted.
Finally, we can use the magnification formula to find the height of the image:
m = h'/h
where h' is the height of the image and h is the height of the object.
Plugging in the values, we get:
m = h'/h
-4 = h'/3
h' = -12cm
Again, the negative sign indicates that the image is inverted. To find the absolute value of the height, we ignore the sign:
| h' | = 12cm
Therefore, the height of the image is 12cm. Answer is correct.