Agar seseorang yang tingginya 160 cm dapat melihat seluruh tubuhnya di depan cermin datar, tinggi...

Summary

In this video, the presenter explains the process of determining the minimum mirror height needed for a person of 160 cm to see their full reflection in a flat mirror. The explanation involves understanding the reflection of light, using angles and congruent triangles to form relationships between the height of the person and the mirror. The key takeaway is that the minimum mirror length required is half the height of the person, which for a 160 cm tall individual results in a mirror length of 80 cm.

Takeaways

• 😀 The problem involves finding the minimum height of a mirror required for a 160 cm person to see their entire body.
• 😀 The solution uses the law of reflection, where the angle of incidence equals the angle of reflection.
• 😀 The person’s body is modeled with points: A (feet), C (head), and B (eyes).
• 😀 The mirror needs to reflect light from both the feet and the head to the eyes for full visibility.
• 😀 The key geometric principle used is that the angle of incidence equals the angle of reflection, applied to light rays from the body to the eyes.
• 😀 The reflection path for light from the feet is analyzed, with the light reflecting at the mirror's edge and traveling towards the eyes.
• 😀 Similarly, light from the head is reflected by the mirror to reach the eyes.
• 😀 Triangles formed by the body’s reflection are used to establish that the length of the mirror is equal to half the person's height.
• 😀 The relationship derived from the geometric analysis is that the required mirror length (l) is half the person’s height (h).
• 😀 For a person with a height of 160 cm, the minimum required mirror length is calculated to be 80 cm.
• 😀 The final answer is that the minimum length of the mirror needed is 80 cm, corresponding to option B in the multiple-choice answers.

Q & A

What is the problem being discussed in the transcript?

The problem discussed is determining the minimum length of a flat mirror required for a person, who is 160 cm tall, to see their entire body in the mirror.

Why is the person’s height important in determining the mirror length?

The person’s height is important because the mirror length needs to be proportional to the person’s height in order to reflect both the lowest and highest points of their body, enabling them to see their full reflection.

How is the geometric setup of the problem described?

The setup involves imagining a mirror with points marked for the lowest and highest parts of the person’s body (feet and head) and considering how light rays reflect off the mirror to reach the person's eyes.

What is the significance of the points A, B, C, D, and E in the explanation?

Points A, B, C, D, and E represent different parts of the person’s body (A for feet, C for head, B for eyes) and the positions on the mirror where light rays are reflected (D and E). These points are used to explain the geometry of light reflection.

What principle of physics is used to determine the mirror length?

The law of reflection, which states that the angle of incidence equals the angle of reflection, is used to derive the necessary conditions for the mirror length.

How are congruent triangles used in this solution?

Congruent triangles are used to simplify the geometric relationships between the various points and angles in the system. This leads to the conclusion that the mirror length must be half the person's height.

What is the formula derived for the mirror length?

The formula derived for the minimum length of the mirror is L = H / 2, where L is the length of the mirror and H is the height of the person.

Why is the mirror length only half the height of the person?

The mirror only needs to be half the person’s height because the light from both the lowest and highest points of the body reflects at angles that only require half the height for the person to see their full reflection.

What conclusion is drawn for a person with a height of 160 cm?

For a person who is 160 cm tall, the minimum mirror length required is 80 cm, as the mirror length is half of the person's height.

What does the result indicate about the minimum length of the mirror?

The result indicates that the mirror needs to cover only the lower half of the person’s height to allow a full-body reflection, highlighting the efficient use of the mirror.