An object 5 cm high is placed at a distance of 60 cm in front of a concane mirror of focal length10cm .Find the position and size of image

To find the position and size of the image formed by the concave mirror, we can use the mirror formula:

1/f = 1/v - 1/u

Where:
f = focal length of the concave mirror
v = image distance (distance of image from the mirror)
u = object distance (distance of object from the mirror)

Given:
focal length (f) = -10 cm (negative for concave mirror)
object distance (u) = -60 cm (negative for object placed in front of the mirror)
height of object (h) = 5 cm

Step 1: Find the position of the image (v):

Using the mirror formula, we have:

1/-10 = 1/v - 1/-60

Simplifying the equation gives:

-1/10 = 1/v + 1/60

Combining the fractions gives:

-1/10 = (60 + v)/60v

Cross multiplying gives:

-6v = 60 + v

Rearranging the equation gives:

7v = 60

Solving for v gives:

v = 60/7 ≈ 8.57 cm

Therefore, the position of the image is approximately 8.57 cm in front of the concave mirror.

Step 2: Find the size of the image (h'):

To find the size of the image, we use the magnification formula:

magnification (m) = -v/u = h'/h

Rearranging the equation gives:

h' = m * h

Here, the magnification (m) can be calculated using:

m = -v/u = -8.57 cm / -60 cm = 0.1428

Substituting the values, we have:

h' = 0.1428 * 5 cm

Calculating the product gives:

h' ≈ 0.714 cm

Therefore, the size of the image is approximately 0.714 cm.

To summarize, the position of the image formed by the concave mirror is approximately 8.57 cm in front of the mirror, and the size of the image is approximately 0.714 cm.