A spherical mirror form a real image 3 times as big as the object. If the focal length of the mirror is 15cm, calculate the distance of image from the mirror. Is the mirror concave or convex?

Question

Answer

Calculating the distance of image from the mirror

Given that:

Magnification (m) = -3 (negative sign indicates that the image is inverted)

Focal length (f) = 15 cm

Using the magnification formula:

m = -v/u

where v is the distance of the image from the mirror and u is the distance of the object from the mirror.

Substituting the values given, we get:

-3 = -v/u

or v/u = 3

Now, using the mirror formula:

1/f = 1/v + 1/u

Substituting the values of f and v, we get:

1/15 = 1/3 + 1/u

Solving for u, we get:

u = 7.5 cm

Therefore, the distance of the image from the mirror is 22.5 cm (since v/u = 3).

Determining the nature of the mirror

Since the image formed is real and inverted, the mirror must be a concave mirror.

A concave mirror is a spherical mirror that curves inward, like the inside of a spoon. When an object is placed in front of a concave mirror, the mirror reflects light rays in such a way that they converge at a point in front of the mirror. This point is called the focus of the mirror.

In this case, since the image formed is real and inverted, the object must be placed beyond the focus of the mirror. As a result, the light rays converge to form a real and inverted image. Since the magnification is greater than 1, the image is also larger than the object.

Answer

The distance of image from the mirror =-60cm
Mirror is concave.

Image is real then magnification =-3 and f=-15cm
m=-v/u from this we will get v=3u
Then use mirror formula you will get.

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