Flag Wave Optics> a plane mirror 50cm long is hung parallel...
question mark

a plane mirror 50cm long is hung parallel to a vertical wall of a room with its lower edge 50cam above the ground. if his eyes were at a height 1.8m above th eground find the length of the floor between him and the mirror visible to him after reflection from the mirror.

kriti , 8 Years ago
Grade 12
anser 1 Answers
Askiitians Tutor Team

Last Activity: 14 Days ago

To solve this problem, we need to visualize the setup and apply some basic principles of geometry and reflection. The plane mirror is positioned parallel to a vertical wall, and we want to determine how much of the floor space between the observer and the mirror is visible to the observer after the reflection. Let's break this down step by step.

Understanding the Setup

We have a plane mirror that is 50 cm long, hung with its lower edge 50 cm above the ground. The observer's eyes are at a height of 1.8 m (or 180 cm) above the ground. The key here is to determine how far the observer can see on the floor between themselves and the mirror.

Key Measurements

  • Height of the observer's eyes: 1.8 m (or 180 cm)
  • Height of the lower edge of the mirror: 0.5 m (or 50 cm)
  • Length of the mirror: 50 cm

Calculating the Reflection

When light reflects off a plane mirror, the angle of incidence equals the angle of reflection. This means that the line of sight from the observer's eyes to the mirror will reflect back to the ground at the same angle. To find the visible length of the floor, we need to determine how far the observer can see down to the mirror and then back to the ground.

Finding the Distance to the Mirror

First, we need to calculate the vertical distance from the observer's eyes to the top edge of the mirror. Since the mirror is 50 cm long and its lower edge is at 50 cm, the upper edge of the mirror is at:

Height of the upper edge of the mirror = 50 cm + 50 cm = 100 cm

Now, the vertical distance from the observer's eyes (180 cm) to the upper edge of the mirror (100 cm) is:

Vertical distance = 180 cm - 100 cm = 80 cm

Using Similar Triangles

Next, we can use similar triangles to find the horizontal distance from the observer to the mirror. The distance from the observer's eyes to the ground is 180 cm, and the distance from the upper edge of the mirror to the ground is 100 cm. The ratio of these distances will help us find the horizontal distance:

Let d be the horizontal distance from the observer to the mirror. The triangles formed by the observer's line of sight to the mirror and the ground are similar:

Height of observer's eyes / Horizontal distance = Height of upper edge of mirror / d

Substituting the known values:

180 / d = 100 / d

Cross-multiplying gives us:

180 * d = 100 * d

Solving for d yields:

d = (180 * d) / 100

Now, we can find the length of the floor visible to the observer. Since the mirror is 50 cm long, the visible length on the floor will be:

Visible length = 2 * d

Final Calculation

To find the exact distance, we can use the height difference and the length of the mirror. The total visible distance on the floor will be:

Visible length = 2 * (180 cm - 100 cm) = 2 * 80 cm = 160 cm

Conclusion

Therefore, the length of the floor visible to the observer after reflection from the mirror is 160 cm. This means that the observer can see a strip of the floor that is 1.6 meters long between themselves and the mirror, thanks to the principles of reflection and geometry.

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments