It is 165 cm from your eyes to your toes. You're standing 200 cm in front of a tall mirror. How far is it from your eyes to the image of your toes?

Verified step by step guidance

Step 1: Understand the problem. The distance from your eyes to your toes is 165 cm, and you are standing 200 cm in front of a mirror. The goal is to determine the distance from your eyes to the image of your toes formed in the mirror.

Step 2: Recall the principle of image formation in a plane mirror. The image of an object in a plane mirror appears to be the same distance behind the mirror as the object is in front of it. This means the image of your toes will be 200 cm behind the mirror.

Step 3: Calculate the total distance from your eyes to the image of your toes. This distance is the sum of the distance from your eyes to the mirror (200 cm) and the distance from the mirror to the image of your toes (200 cm), plus the distance from your eyes to your toes (165 cm).

Step 4: Write the total distance mathematically as: \( \text{Total Distance} = 200 \text{ cm} + 200 \text{ cm} + 165 \text{ cm} \).

Step 5: Add the distances together to find the total distance. This will give you the distance from your eyes to the image of your toes.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Reflection in Mirrors

When light rays hit a mirror, they reflect off the surface according to the law of reflection, which states that the angle of incidence equals the angle of reflection. This means that the image formed in a mirror appears to be the same distance behind the mirror as the object is in front of it. Understanding this principle is crucial for determining the distance from your eyes to the image of your toes.

Distance Measurement

In this scenario, distance is measured from your eyes to the mirror and from the mirror to the image of your toes. The total distance from your eyes to the image can be calculated by adding the distance from your eyes to the mirror and the distance from the mirror to the image, which is equal to the distance from the mirror to your toes. This concept is fundamental for solving the problem accurately.

Geometry of Images

The geometry of images in mirrors involves understanding how the position of an object relates to its image. In a flat mirror, the image appears to be the same size as the object and is located directly behind the mirror at an equal distance. This geometric relationship helps in visualizing and calculating the distance from your eyes to the image of your toes in the given scenario.

Recommended video:

07:58

Thin Lens Equation

Related Practice

Textbook Question

At what angle ϕ should the laser beam in FIGURE EX34.6 be aimed at the mirrored ceiling in order to hit the midpoint of the far wall?

views

Textbook Question

A 1.0-cm-thick layer of water stands on a horizontal slab of glass. A light ray in the air is incident on the water 60° from the normal. What is the ray's direction of travel in the glass?

views

Textbook Question

A costume jewelry pendant made of cubic zirconia is submerged in oil. A light ray in the oil strikes one face of the zirconia crystal at an angle of incidence of 25°. Once inside, what is the ray's angle with respect to the face of the crystal?

views

Textbook Question

The mirror in FIGURE EX34.5 deflects a horizontal laser beam by 60°. What is the angle ϕ?

Textbook Question

When you look into your car's 5.0-cm-tall rear-view mirror from 35 cm away, the front of a bus, from the ground to the roof, exactly fills the mirror. If the bus is 17 m from the mirror, how tall is the bus?

Textbook Question

The glass core of an optical fiber has an index of refraction 1.60. The index of refraction of the cladding is 1.48. What is the maximum angle a light ray can make with the wall of the core if it is to remain inside the fiber?

views