Understanding Image Formation by Convex and Concave Mirrors: A Comprehensive Guide

When light rays hit a reflecting surface, they can create either real or virtual images. Convex and concave mirrors are two types of reflecting surfaces that create distinct types of images. In this guide, we will explore the process of image formation by convex and concave mirrors through the use of the mirror formula and a detailed analysis of image properties.

Convex Mirror: Image Formation at 10 cm from the Mirror

Consider an object placed at a distance of 10 cm from a convex mirror with a focal length of 15 cm. To find the position and nature of the image, we use the mirror formula:

1/v 1/u 1/f

Given that the focal length of a convex mirror is always negative:

f -15 cm

Substituting the given values into the mirror formula:

1/v 1/10 -1/15

Solving for 1/v:

1/v -1/10 - 1/15 -3/30 - 2/30 -5/30 -1/6

Therefore, v -6 cm

The negative sign of v indicates that the image is virtual and located inside the mirror. Thus, a virtual image will form 6 cm inside the convex mirror.

Concave Mirror: Image Formation at 10 cm Slightly Adjusted

Now, let's consider a concave mirror with the same object distance but a different focal length. Suppose the focal length is still 15 cm but the object is slightly closer to the mirror, so the object distance is -10 cm. To find the image distance, we again use the mirror formula:

1/v 1/u 1/f

Where:

u -10 cm
f -15 cm

Substituting these values into the mirror formula:

1/v 1/-10 1/-15

Simplifying:

1/v -1/15 1/10 -2/30 3/30 1/30

Therefore, v 30 cm

The positive sign of v indicates that the image is real and located behind the mirror. The image is erect and magnified as the magnification m v/u 30/-10 -3.

Summary of Image Formation

In summary, the nature and position of the image formed by convex and concave mirrors can be determined using the mirror formula:

Convex Mirror

Positive v indicates a virtual image that appears behind the mirror. Negative v indicates a virtual image that appears inside the mirror. The image is always erect and smaller than the object.

Concave Mirror

Positive v indicates a real image that appears behind the mirror. Negative v indicates a virtual image that appears in front of the mirror. The image can be real or virtual, depending on the object distance.

The formation of images by convex and concave mirrors is a fundamental concept in optics, with applications in everyday life and scientific research. Understanding how to use the mirror formula accurately is crucial for predicting the behavior of light and visual phenomena.