Mirrors - Plane Mirror

A plane mirror is a flat and smooth glass surface coated on the back with a thin reflective layer of aluminium or silver. This reflective layer is protected with a coat of materials like lead oxide, which also makes the surface opaque. Plane mirrors are widely used in our daily lives, such as in household mirrors, where we see a clear reflection of ourselves.

• When light rays from a point source hit the mirror, they reflect and reach our eyes. Due to the reflection, these rays appear to be coming from a point behind the mirror, creating the image of the point source. This simple principle of reflection makes plane mirrors essential for forming clear and accurate images.
• The image created by a plane mirror has several unique characteristics: it appears to be the same size as the object, is laterally inverted (left and right are reversed), and is located behind the mirror at the same distance as the object is in front of it.
• Plane mirrors are commonly used in everyday life, such as in bathrooms and dressing rooms, and are essential for understanding basic concepts of light reflection and image formation.

Reflection of Light:

As shown in Figure A, light rays falling perpendicular to a mirror are reflected back along the same path. This is due to the laws of reflection, where the angle of incidence equals the angle of reflection.

Image of a Point Source:

In Figure B, a point source O is placed in front of the plane mirror M₁M₂​.

• Light rays OR₁​ and OR₂​ hit the mirror and reflect as R₁S₁​ and R₂S₂​, following the laws of reflection.
• When these reflected rays are extended behind the mirror, they appear to meet at O₁​, forming the virtual image of the point source.
• The reflected rays do not actually meet; hence, the image is virtual and cannot be captured on a screen.
• The distance of the image from the mirror is the same as the distance of the source from the mirror.

Image of an Extended Source:

As shown in Figure C, when an extended source PQ is placed in front of the mirror M₁M₂​:

• The image of P is formed at P₁​, and the image of Q is formed at Q₁.
• Similarly, every point between P and Q forms corresponding points between P₁​ and Q_1​, creating an extended image P₁Q₁​.

Characteristics of the Image:

The image is of the same size as the source, is formed behind the mirror and is virtual.

The image undergoes lateral inversion:

• For example, the word "MIRROR" appears reversed when seen in the mirror.
• Every point on the source is reflected at an equal distance behind the mirror, maintaining symmetry.

Formation of images by a mirror

To observe the properties of an image formed by a plane mirror, including its orientation, size, and distance from the mirror.

• Stand in front of a plane mirror and observe your reflection.
• Raise your right hand, and notice that the mirror image raises its left hand. This is called lateral inversion, where left and right appear reversed.
• Move closer to the mirror, and the image also appears to move closer. Move farther, and the image moves farther as well.
• Compare your height with the image in the mirror—it remains the same size as the actual object.
• The image is formed behind the mirror at the same distance as the object is in front of it.
• A plane mirror forms a laterally inverted, same-sized, and virtual image that maintains the same distance from the mirror as the object.

The image in a plane mirror

1. Aim: To study the number of images formed by two plane mirrors placed at different angles.

2. Requirements: Two plane mirrors, a small object, and a protractor to measure the angle between the mirrors.

3. Procedure

• Place the two plane mirrors at an angle of 90° to each other.
• Position a small object between the mirrors. Observe and count the number of images formed in the mirrors.
• Change the angle between the mirrors to different values (120°, 60°, 45°, 30°) and count the images for each angle.

\[\begin{gathered}
\mathrm{For~A}=120^\circ{:}n=\frac{360}{120}-1=2 \\
\mathrm{For~A}=90^\circ{:}n=\frac{360}{90}-1=3 \\
\mathrm{For~A}=60^\circ:n=\frac{360}{60}-1=5 \\
\mathrm{For~A}=45^\circ{:}n=\frac{360}{45}-1=7 \\
\mathrm{For~A}=30^{\circ}:n=\frac{360}{30}-1=11
\end{gathered}\]

Use the formula n= \[\mathrm{n}=\frac{360^0}{\mathrm{A}}-1\] , where n is the number of images and A is the angle between the mirrors, to verify the observations. Repeat the experiment with the mirrors placed parallel to each other and count the number of images formed.

Mirrors at right angles to each other

3. Observation Table

4. Conclusion: The number of images formed by two mirrors increases as the angle between them decreases. When the mirrors are parallel, an infinite number of images are formed. The relationship between the angle and the number of images is consistent with the formula n=\[\mathrm{n}=\frac{360^0}{\mathrm{A}}-1\].

Statement: To see the full image of a person standing in front of a mirror, the minimum height of the mirror must be half the height of the person.

Proof:

1. Explanation Using Points

The points on a person are labelled as follows:

• H: Top of the head.
• E: Eyes.
• F: Feet.

R and S are the midpoints of HE and EF, respectively. The mirror PQ is placed perpendicular to the ground, with the bottom point N.

2. Reflection of Light

For the full image to be visible, light rays from the top of the head (H) and feet (F) must reflect into the observer’s eyes after striking the mirror. The rays RP (from H) and SQ (from F) must meet the mirror at points that allow perpendicular reflections.

Calculation: The height of the mirror PQ must cover the segments RE and ES, which are each half of their respective segments:

RE=`"HE"/"2"`

ES=`"EF"/"2"`

Adding these together:

PQ=RE+ES=`"HE"/"2"`+`"EF"/"2"`

=`"HF"/"2"`=Half of the person’s height

Therefore, PQ (the minimum height of the mirror) equals half the height of the person (HF).

Conclusion: The minimum height of a mirror required to see a person’s full image is half the height of the person. This ensures that the light rays from the top and bottom points of the person reflect properly into the observer's eyes.

A plane mirror and the full image of a person