Which one of the following statements is correct for a plane mirror?
The image is virtual, erect and laterally inverted
Understanding Plane Mirror Properties
A plane mirror is a flat reflective surface. When an object is placed in front of a plane mirror, an image is formed behind the mirror. The characteristics of this image are consistent and follow specific rules of reflection.
Analyzing the Properties of a Plane Mirror Image
Let's examine the common properties of an image formed by a plane mirror:
- Nature: The image is always virtual. This means that the light rays do not actually converge at the image location; they only appear to originate from there. A virtual image cannot be projected onto a screen.
- Orientation: The image is always erect (or upright). This means that if the object is placed vertically, the image is also vertical with the top at the top and the bottom at the bottom.
- Size: The size of the image is always the same as the size of the object.
- Distance: The distance of the image behind the mirror is always equal to the distance of the object in front of the mirror.
- Inversion: The image is laterally inverted. This means that the image is flipped left-to-right compared to the object. For example, if you raise your right hand, your image in a plane mirror appears to raise its left hand.
Evaluating the Given Statements about Plane Mirrors
Now, let's look at the provided options and determine which statement correctly describes a plane mirror.
Option 1: Its focal length is zero.
For a spherical mirror, the focal length (\(f\)) is half of the radius of curvature (\(R\)), i.e., \(f = R/2\)). A plane mirror can be considered a part of a sphere with an infinitely large radius of curvature (\(R \to \infty\)). Therefore, the focal length of a plane mirror is also infinite (\(f = \infty/2 = \infty\)). This statement is incorrect.
Option 2: The size of the image of an object placed in front of the mirror is slightly less than that of the object.
As discussed, the image formed by a plane mirror is always of the same size as the object. There is no magnification or minification. This statement claims the image is slightly less, which is incorrect.
Option 3: The image is virtual, erect and laterally inverted.
This statement lists three key properties of the image formed by a plane mirror: virtual nature, erect orientation, and lateral inversion. All three of these are correct characteristics of a plane mirror image. This statement is correct.
Option 4: Its focal length is 200 cm.
As established when evaluating Option 1, the focal length of a plane mirror is infinite, not a finite value like 200 cm. This statement is incorrect.
Based on the analysis of each statement and the known properties of plane mirrors, the correct statement is that the image is virtual, erect, and laterally inverted.
Revision Table: Plane Mirror Properties
| Property | Description for Plane Mirror |
|---|---|
| Nature of Image | Virtual |
| Orientation of Image | Erect (Upright) |
| Size of Image | Same as Object Size |
| Distance of Image | Equal to Object Distance (behind the mirror) |
| Lateral Inversion | Yes (left and right are flipped) |
| Focal Length | Infinite (\(\infty\)) |
| Radius of Curvature | Infinite (\(\infty\)) |
Additional Information on Reflection
Reflection is the phenomenon where light bounces off a surface. Plane mirrors reflect light according to the laws of reflection:
- The angle of incidence is equal to the angle of reflection (\(\theta_i = \theta_r\)).
- The incident ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane.
These laws govern how the image is formed in a plane mirror, resulting in the specific properties observed, such as the image being virtual, erect, and laterally inverted, and located at the same distance behind the mirror as the object is in front.
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