AN OBJECT OF HEIGHT 5CM IS PLACED INFRONT OF ACONCAVE MIRROR OF FOCAL LENGTH 6CM AT ADISTANCE OF 13CM .FIND IMAGE SIZE
To find the image size for an object placed in front of a concave mirror, you 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:
focal length (f) = -6 cm (negative because it is a concave mirror)
object distance (u) = -13 cm (negative because the object is placed in front of the mirror)
To find the image distance, v, you can rearrange the mirror formula:
1/v = 1/f - 1/u
Substituting the given values:
1/v = 1/-6 - 1/-13
Now, let's solve this equation step by step:
1/v = -13/(-6)(-1) - 6/(-13)(-1)
Simplifying the equation:
1/v = 13/6 + 6/13
To add fractions with different denominators, we need to find a common denominator:
1/v = (13/6)(13/13) + (6/13)(6/6)
1/v = 169/78 + 36/78
1/v = 205/78
Now, reciprocate both sides of the equation to find v:
v = 78/205
Therefore, the image distance (v) is approximately 0.38 cm.
To find the magnification (m) of the mirror, you can use the formula:
m = -v/u
Given:
v = 0.38 cm
u = -13 cm
Substituting the values:
m = -0.38/(-13)
Simplifying the equation:
m = 0.38/13
Therefore, the magnification (m) is approximately 0.029.
To find the image size, you can use the magnification formula:
m = h'/h
Where:
m = magnification
h' = image height
h = object height
Given:
m = 0.029 (rounded from previous calculation)
h = 5 cm
Rearranging the formula:
h' = m * h
Substituting the values:
h' = 0.029 * 5
Therefore, the image size (h') is approximately 0.145 cm.