Understanding Image Distance in Plane Mirrors

This problem involves the principles of reflection in a plane mirror, specifically how the distance of an object from the mirror relates to the distance of its image from the mirror, and consequently, the distance between the object and its image.

Key Principle of Plane Mirrors

A fundamental property of images formed by a plane mirror is that the distance of the image behind the mirror is equal to the distance of the object in front of the mirror. This is often stated as:

\( \text{Object distance} = \text{Image distance} \)

If we denote the object distance as \(u\) and the image distance as \(v\), then for a plane mirror, \(u = v\).

The distance between the object and its image in a plane mirror is therefore \(u + v = u + u = 2u\).

Step-by-Step Solution

Let's break down the problem into two parts: the initial situation and the situation after the lady walks towards the mirror.

Initial Position Calculation

• The lady is initially standing at a distance of 1 m from the plane mirror.
• Initial object distance, \(u_1 = 1 \text{ m}\).
• Since the image distance equals the object distance in a plane mirror, the initial image distance is also \(v_1 = 1 \text{ m}\).
• The initial distance between the lady (object) and her image is \(u_1 + v_1 = 1 \text{ m} + 1 \text{ m} = 2 \text{ m}\).

Movement Towards the Mirror

• The lady walks 60 cm towards the mirror.
• We need to work with consistent units. Let's convert 60 cm to meters.
• Conversion: \(1 \text{ m} = 100 \text{ cm}\). Therefore, \(60 \text{ cm} = \frac{60}{100} \text{ m} = 0.60 \text{ m}\).

Final Position Calculation

• After walking 0.60 m towards the mirror, her new distance from the mirror is the initial distance minus the distance she walked.
• New object distance, \(u_2 = u_1 - (\text{distance moved}) = 1 \text{ m} - 0.60 \text{ m} = 0.40 \text{ m}\).
• Again, for a plane mirror, the new image distance will be equal to the new object distance.
• New image distance, \(v_2 = u_2 = 0.40 \text{ m}\).
• The new distance between the lady (object) and her image is \(u_2 + v_2 = 0.40 \text{ m} + 0.40 \text{ m} = 0.80 \text{ m}\).

Converting to Centimeters

The options are given in centimeters. Let's convert the final distance from meters to centimeters.

\(0.80 \text{ m} = 0.80 \times 100 \text{ cm} = 80 \text{ cm}\).

So, the distance of her image now from herself is 80 cm.

Summary of Distances

Revision Table: Plane Mirror Image Properties

Additional Information about Plane Mirror Reflection

Plane mirrors form images through regular reflection. When light rays from an object strike the mirror surface, they reflect according to the laws of reflection. For each point on the object, reflected rays appear to diverge from a point behind the mirror. This point is where the virtual image is located.

• Virtual Image: The image cannot be projected onto a screen. The light rays do not actually converge at the image location; they only appear to originate from there.
• Erect Image: The image is oriented the same way as the object (upright).
• Same Size: The magnification is +1 for a plane mirror.
• Lateral Inversion: While the image is erect vertically, it is flipped horizontally. For example, if you raise your right hand, your image in the mirror raises its left hand.

Understanding these properties is crucial for solving problems involving plane mirrors and how distances change with object movement.