Understanding Image Formation by a Convex Lens: A Practical Guide

Introduction

A convex lens is an optical element that converges light to form images. To understand how an image is formed by a convex lens, we use the lens formula:

Lens Formula and Its Components

The lens formula is given by the equation:

[frac{1}{f} frac{1}{v} - frac{1}{u}]

where:

f is the focal length of the lens (positive for a convex lens). v is the image distance from the lens. u is the object distance from the lens (negative in the lens formula convention).

Solving for Image Distance

Let's consider an object placed at a distance of 30 cm from a convex lens with a focal length of 20 cm. We need to find the position of the image:

Given data:

f 20 cm (positive for a convex lens). u -30 cm (the object is placed on the opposite side of the light entering the lens).

Rearrange the lens formula to solve for v:

[frac{1}{v} frac{1}{f} - frac{1}{u}]

Substituting the given values:

[frac{1}{v} frac{1}{20} - frac{1}{-30}]

A common denominator for 20 and -30 is 60:

(frac{1}{20} frac{3}{60}) (frac{1}{-30} frac{-2}{60})

Substitute these values into the equation:

[frac{1}{v} frac{3}{60} - frac{-2}{60} frac{5}{60}]

Now, taking the reciprocal to find v:

[v frac{60}{5} 12,text{cm}]

Conclusion: The image is formed at a distance of 60 cm on the opposite side of the lens from the object. Since v is positive, the image is real and inverted.

Additional Scenarios

Image behind a convex mirror: The image is located 12 cm behind the mirror. Since v is positive, the image is virtual and erect. Object half a focal length outside its focal point: The magnification is M -2, and the image is 2 focal lengths outside the focal point, which is a 60 cm distance to the lens. Further clarification: According to the convention, real distances are positive. For a convex lens, an image is real if Do f. In this case, the object distance Do is 30 cm, and the focal length f is 20 cm, so Do f. Therefore, we expect a real image. Known limitations: A convex mirror cannot form an image. You would need a concave mirror to form an image.

Conclusion

Understanding image formation by a convex lens is crucial in optics. By using the lens formula, we can calculate the position, nature, and size of the image. Various scenarios further illustrate the application and limitations of the convex lens in different optical systems.