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An Object 2cm High Is Placed At A Distance Of 16cm From A Concave Mirror

4 min read Sep 04, 2024
An Object 2cm High Is Placed At A Distance Of 16cm From A Concave Mirror

An Object 2cm High is Placed at a Distance of 16cm from a Concave Mirror

This scenario describes a basic setup in optics, where a concave mirror is used to form an image of an object. Let's explore the key concepts and calculations involved.

Understanding Concave Mirrors

Concave mirrors are curved inward, like the inside of a spoon. They have a focal point (F) and a center of curvature (C), both located on the principal axis.

  • Focal Point (F): The point where parallel rays of light converge after reflecting off the mirror.
  • Center of Curvature (C): The center of the sphere from which the mirror is a part.

Key Concepts and Formulas

  • Object Distance (u): The distance between the object and the mirror. In this case, u = -16cm (negative sign indicates the object is placed in front of the mirror).
  • Image Distance (v): The distance between the image and the mirror.
  • Focal Length (f): The distance between the focal point and the mirror.
  • Magnification (M): The ratio of the image height (h') to the object height (h).

We can use the mirror formula to relate these quantities:

1/f = 1/u + 1/v

And the magnification formula:

M = h'/h = -v/u

Determining the Image Characteristics

To determine the image characteristics, we need to know the focal length (f) of the concave mirror. Let's assume the focal length is f = 8cm.

  1. Calculating Image Distance (v):

    Using the mirror formula:

    1/8 = 1/-16 + 1/v

    Solving for v, we get:

    v = 16 cm

  2. Calculating Magnification (M):

    Using the magnification formula:

    M = -16/(-16) = 1

  3. Image Characteristics:

    • Image Distance: The image is formed at a distance of 16cm behind the mirror (positive v).
    • Magnification: The magnification is +1. This indicates that the image is the same size as the object (h' = h = 2cm).
    • Nature of Image: Since the magnification is positive and the image is formed behind the mirror, the image is real, inverted, and the same size as the object.

Conclusion

In this scenario, the concave mirror forms a real, inverted, and the same size image of the object. This outcome is specific to the given focal length (f = 8cm) and object distance (u = -16cm). Changing these parameters would affect the image characteristics.

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