a 2cm high object is placed at a distance of 20cm from concave mirror ,the real image is formed at 40cm from the mirror.calculate the focal length,size of image and magnification?

answer

To solve this problem, we can use the mirror equation:

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.

Given:
u = -20 cm (negative because it's in front of the mirror)
v = 40 cm
We need to find f, the size of the image, and the magnification.

Step 1: Calculating the focal length (f)
We can rearrange the mirror equation to solve for f:

1/f = 1/v - 1/u

1/f = 1/40 - 1/-20

1/f = (2 - (-1)) / 40
1/f = 3/40

f = 40/3 cm

Step 2: Calculating the size of the image
To find the size of the image, we can use the magnification formula:

magnification (m) = -v/u = height of image/height of object

Since the object height is given as 2 cm, we can rearrange the equation to solve for the height of the image:

height of image = magnification * height of object

magnification (m) = -40/(-20) = 2

height of image = 2 * 2 cm = 4 cm

Therefore, the size of the image is 4 cm.

Step 3: Calculating the magnification (m)
We've already calculated the magnification in Step 2 using the formula:

magnification (m) = -v/u = height of image/height of object

magnification (m) = -40/-20 = 2

Thus, the magnification is 2.

In summary:
Focal length (f) = 40/3 cm
Size of image = 4 cm
Magnification (m) = 2