Height of object is 1 cm placed at a distance of 15 cm from a concave mirror of focal length 10 cm. Find nature, size and position
To find the nature, size, and position of the image formed by a concave mirror, we can use the mirror formula:
1/f = 1/v - 1/u
where:
f = focal length of the mirror
v = image distance from the mirror
u = object distance from the mirror
Given:
f = -10 cm (negative sign for concave mirror)
u = -15 cm (negative sign indicates object is placed in front of the mirror)
h = 1 cm (object height)
First, let's find the position and size of the image:
1/f = 1/v - 1/u
Substituting the values:
1/-10 = 1/v - 1/-15
Simplifying:
-1/10 = 1/v + 1/15
Combining the terms:
-15/150 = 15/v + 10/v
Simplifying further:
-15/150 = (15 + 10)/v
-15/150 = 25/v
Cross-multiplying:
-15v = 25 * 150
Dividing both sides by -15:
v = -25 * 150 / -15
v = 250 cm
The image distance (v) is positive, indicating that the image is formed on the opposite side of the mirror from the object.
To find the magnification (m), we can use the formula:
m = -v/u
Substituting the values:
m = -250 / -15
m = 16.67
The magnification (m) is positive, indicating that the image is upright.
To find the height of the image (h'), we can use the formula:
h' = m * h
Substituting the values:
h' = 16.67 * 1
h' = 16.67 cm
The height of the image (h') is positive, indicating that the image is upright and larger than the object.
Therefore, the nature of the image formed by the concave mirror is a virtual, erect, and magnified image located at a distance of 250 cm from the mirror. The size of the image is 16.67 cm.