An object is placed 20cm from a concave mirror of focal length 15cm. Calculate the linear magnification of the image formed
Answer Details
The linear magnification of an image formed by a spherical mirror is given by the formula:
magnification = height of image / height of object = -v/u
where u is the object distance, v is the image distance and the negative sign indicates that the image is inverted.
Given that the object is placed 20cm from a concave mirror of focal length 15cm, we can use the mirror formula:
1/f = 1/u + 1/v
Rearranging this formula, we get:
1/v = 1/f - 1/u
Substituting the given values, we get:
1/v = 1/15 - 1/20
1/v = (4 - 3)/60
1/v = 1/60
v = 60 cm
Now, the magnification can be calculated as:
magnification = -v/u = -60/20 = -3
Therefore, the linear magnification of the image formed is 3. Since the image is inverted, the sign of the magnification is negative. So, the correct answer is (d) 3.0.