A point object is placed between a plane mirror and concave mirror facing each other. The distance between the mirrors is 22.5 cm. Plane mirror is placed perpendicular to the principal axis of concave mirror. ?

Question

Answer

Understanding the Problem

A point object is placed between a plane mirror and concave mirror facing each other. The distance between the mirrors is 22.5 cm. Plane mirror is placed perpendicular to the principal axis of concave mirror.

Solution

Let us first understand the diagram.

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As shown in the diagram, a point object is placed between a plane mirror and a concave mirror facing each other. The distance between the mirrors is given as 22.5 cm. The plane mirror is placed perpendicular to the principal axis of the concave mirror.

What happens when light rays fall on the mirrors?

When light rays fall on the plane mirror, they reflect back in the opposite direction, forming an image behind the mirror.

When light rays fall on the concave mirror, they converge at a point called the focus.

When light rays from a point object fall on the concave mirror, they converge at a point called the image point.

Where is the image formed?

The image formed in this case is the virtual image formed by the plane mirror.

The virtual image is formed behind the mirror at the same distance as the object is placed in front of the mirror.

Hence, the virtual image is formed at a distance of 22.5 cm behind the plane mirror.

What is the final image?

Now, the light rays from the virtual image formed by the plane mirror act as the object for the concave mirror.

These light rays converge at a point called the focus of the concave mirror.

Thus, the final image is formed at the focus of the concave mirror.

What is the distance of the final image from the concave mirror?

The distance of the final image from the concave mirror can be calculated using the mirror formula:

1/f = 1/v + 1/u

Where f is the focal length of the concave mirror, v is the distance of the final image from the concave mirror, and u is the distance of the object from the concave mirror.

Since the object is at the focus of the concave mirror, u = f.

Substituting the values, we get:

1/f = 1/v + 1/f

1/v = 1/f - 1/f

1/v = 0

v = infinity

Hence, the final image is formed at infinity from the concave mirror.

Conclusion

In this problem, we have seen how a virtual image formed by a plane mirror can act as an object for a concave mirror, and how the final image is formed at the focus of the concave mirror at infinity.

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