Virtual Images

Introduction

A virtual image is a type of image formed when the outgoing rays from a point on an object diverge. The apparent intersection of these diverging rays occurs behind the plane of the mirror or lens, thus giving the illusion that light comes from this intersection point, even though the light is actually diverging.

Definition of Virtual Images

Virtual images are formed by the apparent intersection of light rays. Unlike real images, which are formed by actual convergence of light rays, virtual images cannot be projected onto a screen. However, they can still be seen by an observer looking through the lens or at the mirror.

Virtual Images in Mirrors

In a plain mirror, the image formed is always virtual. The object distance (distance from the object to the mirror) is the same as the image distance (distance from the image to the mirror). The image is the same size as the object and is laterally inverted (flipped left to right).

Virtual Images in Lenses

Virtual images can be formed by lenses under certain conditions. For a converging lens, a virtual image is formed when the object is placed within the lens’s focal length. For a diverging lens, the image formed is always virtual, regardless of the object’s location.

Lensmaker’s Equation

The Lensmaker’s Equation relates the focal length of a lens to the radii of curvature of its two surfaces and the refractive index of the lens material. This equation is given by:

where:

• is the focal length of the lens,
• is the refractive index of the lens material,
• and are the radii of curvature of the lens surfaces.

Mirror and Lens Equations

In geometric optics, the mirror and lens equations help us determine the location and nature of the image formed. For a mirror, the equation is:

where:

• is the focal length of the mirror or lens,
• is the object distance,
• is the image distance.

For a thin lens, the equation is the same.

For virtual images, is considered to be negative.

Magnification

The magnification of the image formed by a mirror or lens can be determined using the magnification equation:

where:

• is the magnification,
• is the image distance,
• is the object distance.

If the magnification is negative, the image is inverted. If the magnification is less than 1, the image is reduced in size; if the magnification is greater than 1, the image is enlarged. For virtual images, the magnification is positive, indicating that the image is upright.

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