An object 7.5cm high is placed 30cm from a concave mirror of radius 20cm,calculate the image distance and image height
To solve this problem, we can use the mirror formula and magnification formula.
1. The mirror formula:
1/f = 1/v - 1/u
Where f is the focal length of the mirror, v is the image distance, and u is the object distance.
2. The magnification formula:
magnification = -v/u
Negative sign indicates that the image is inverted.
Now, let's substitute the given values into the equations:
u = -30cm (negative sign indicates the object is placed in front of the mirror)
f = -20cm (negative sign indicates a concave mirror)
v = ?
magnification = ? (Later, we can use this value to calculate the image height)
Using the mirror formula:
1/f = 1/v - 1/u
1/-20 = 1/v - 1/-30
-1/20 = 1/v + 1/30
(-1/20) - (1/30) = 1/v
-3/60 - 2/60 = 1/v
-5/60 = 1/v
v = -60/5
v = -12cm
Now we have the value for v (image distance).
Using the magnification formula:
magnification = -v/u
magnification = -(-12)/(-30)
magnification = 12/30
magnification = 0.4
The magnification tells us that the image is 0.4 times the size of the object.
To calculate the image height, we can use the magnification formula:
magnification = image height / object height
0.4 = image height / 7.5cm
Rearranging the equation to solve for the image height:
image height = magnification x object height
image height = 0.4 x 7.5cm
image height = 3cm
Therefore, the image distance is -12cm (which indicates that the image is formed on the same side as the object) and the image height is 3cm.