what is sign of the object distance u when an object is placed before a concave mirror ?

When dealing with concave mirrors in optics, the sign convention for object distance, denoted as "u," is quite specific. For a concave mirror, when an object is placed in front of it, the object distance is considered negative. This is based on the Cartesian sign convention used in optics, where distances measured in the direction of the incoming light (toward the mirror) are taken as negative.

Understanding Object Distance in Concave Mirrors

To grasp why the object distance is negative, let’s break it down step by step:

The Basics of Concave Mirrors

A concave mirror is a spherical mirror that curves inward, resembling a portion of a sphere. When light rays strike this type of mirror, they converge or focus at a point known as the focal point. The behavior of light with concave mirrors is crucial in various applications, such as in telescopes and shaving mirrors.

Sign Convention Explained

• Object Distance (u): This is the distance from the mirror to the object being reflected. According to the sign convention, this distance is negative when the object is in front of the mirror.
• Image Distance (v): This is the distance from the mirror to the image formed. It is positive if the image is formed on the same side as the object (real image) and negative if on the opposite side (virtual image).
• Focal Length (f): For concave mirrors, the focal length is also negative, as it is measured from the mirror to the focal point, which lies in front of the mirror.

Why the Negative Sign?

The negative sign for the object distance arises from the way we define our coordinate system. In optics, we typically set the mirror's surface as the origin (0 point). Distances measured in the direction of the incoming light (toward the mirror) are assigned negative values, while distances measured away from the mirror (in the direction of the reflected light) are positive. Since the object is placed in front of the mirror, it falls into the negative distance category.

Practical Example

Imagine you have a concave mirror and you place an object, like a candle, 10 cm in front of it. According to the sign convention:

• The object distance (u) = -10 cm.

When you use the mirror formula, which is:

1/f = 1/v + 1/u

Here, you would substitute -10 cm for u, allowing you to calculate the image distance (v) and determine the nature of the image (real or virtual).

Conclusion

In summary, when an object is placed before a concave mirror, the object distance "u" is negative. This is a fundamental aspect of the sign convention in optics, which helps in accurately predicting the behavior of light and the characteristics of the images formed by mirrors. Understanding this concept is essential for further studies in optics and related fields.