A concave mirror forms a real image having the same size as the object at a distance of 40 cm in front of the mirror . What is the focal length of the mirror.
Answers
Since focal length of concave mirrorgiven is 20cm l. Object is at 40cm distance which means it is at centre of curvature. hence, image will be formed of same size and at centre focus only but real and inverted.
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The mirror is concave, i.e., it is diverging. Since the rays from infinity do not converge to form a real image, but instead appear to diverge, we use the notation that the focal length is negative, i.e., f = -40cm.
Now intuitively analyse, under what conditions can a concave mirror produce a magnified image? That would happen when the object lies close to the mirror and the image is formed farther away.
Magnification is the ratio of the height of the image to the height of the object. This is also equal to the negative of the ratio between the image distance and the object distance.
m = height(image) / height(object) = −v / u
m = 4 => v = -4u
Substitute in the mirror formula:
1/f = 1/u −1/4u
Solve this to get u = -30 cm.
Then find v = -4u = 120 cm, which is to the right of the mirror( Assuming that the ray is incident on the mirror from the left side)
This matches the intuition that a virtual, erect and magnified image is obtained in a concave mirror when the object is placed between F and P(Pole of the mirror). The resulting image is formed ‘behind the mirror’.