Dikshant SavantApr 14, 2026
Calculating Minimum Mirror Size 📐
5views
Calculating Minimum Mirror Size 📐
Dikshant Savant
Learn how to calculate the minimum mirror size required to see a full reflection using geometric principles and similar triangles. This tutorial breaks down the math behind mirror physics with clear, step-by-step examples.
Calculating Minimum Mirror Size 📐
Dikshant Savant
Learn how to calculate the minimum mirror size required to see a full reflection using geometric principles and similar triangles. This tutorial breaks down the math behind mirror physics with clear, step-by-step examples.
Chapters
00:00
Introduction
Introduction to the problem of calculating mirror size for viewing.
00:12
Problem Setup
01:26
Geometric Calculation
03:06
Step-by-Step Math
07:12
Second Scenario Analysis
08:06
General Rule Conclusion
Transcript
00:00
Hello.
00:01
I saw this question, okay?
00:03
And, this is pretty interesting.
00:05
Okay, so let's take a look at this.
00:07
Okay, I'll just take some example values and just show you how this can be done.
00:12
Okay, so let's say this person is 100 cm tall, for example, too small, but let's say.
00:23
And the dog is 10 centimeter tall.
00:26
Basically, his eyes are over here of the dog at 10 centimeters.
00:31
And there's a mirror over here.
00:33
Now, it also depends on what is the distance of this mirror.
00:38
Let's say here, this is, let's say 50 centimeters.
00:43
And, this is also 50 centimeters.
00:47
So essentially what is happening is for this, dog to see the top of the head of this person, a light ray has to come from here, hit the mirror, and then come to the eyes.
01:05
Right?
01:07
And, this is the same process of how the foot will also show.
01:14
Like let's say this is the foot of the person.
01:16
So light ray comes over here, bounces.
01:21
Okay.
01:21
Okay.
01:22
My diagrams are not that pretty, but okay, this is how it's going to happen, right?
01:26
So essentially you'll have to use a little bit of trigonometry or some similar triangles.
01:31
so what is happening is, this is 90, centimeters, right?
01:39
This is 90 centimeters from here to here.
01:42
And distance, total traveled is 100 centimeters.
01:46
So essentially the mirror.
01:48
Okay, how much is the mirror that is required?
01:51
See, the mirror, the minimum length of the mirror is only this much because the top ray comes over here and the bottom ray comes over here.
02:00
So if I'm able to find this length of the mirror, let's say call this X, that will be my answer.
02:06
Right?
02:07
So how do I calculate this?
02:10
Basic, trigonometry or like similar triangles.
02:14
Say.
02:16
Okay, so this is 50 centimeters, right?
02:20
And, Okay, so let's do this.
02:26
Since these two triangles are similar, this length, let's say, okay, and this length from, here is 10 centimeters.
02:40
Let me make like a better diagram for this.
02:45
So this is 100, this is 10.
02:51
And this is the mirror.
02:54
And here we have to find the length of this mirror.
03:00
So, okay, let's do this simply.
03:06
yeah, so one ray is coming over here like this.
03:11
And so if I can find this length first let's find this length.
03:19
This length will be how much?
03:23
So this is 50, this is 50, and here it's 10.
03:32
So that means.
03:37
So since this is 50 and this is also 50.
03:53
Okay, so we can think it like this.
04:01
Yeah, so it takes, 50 centimeter.
04:06
50 centimeter.
04:07
And 50 more centimeter to rise to a height of 10 centimeter.
04:12
That means 150 centimeters traveled in this direction to go up 10 centimeters.
04:19
Right.
04:20
So how much up does will it travel if it only had to travel 100 centimeters, basically, what is this height?
04:27
So, so 1 centimeter traveled is 10 over 150 centimeters.
04:33
That means 100 centimeters travel in this direction will be 10 over 150 into 100 and which basically gives us this much 100 over 15.
04:45
we'll simplify this later, but essentially we have this length.
04:48
Okay.
04:48
100 over 15.
04:50
Or we can say 525.
04:52
3 is a 6.33 centimeters.
04:56
Okay.
04:57
Or, 6, uh,.66.
04:59
Right.
05:00
6.66 centimeters.
05:02
Okay, now to, find this length top of the mirror to over here, we'll use the similar unitary method where, essentially, the ray has traveled basically 90 centimeters down.
05:22
Right?
05:22
So it has traveled, Yeah, let me do that calculation also.
05:27
It has traveled 150 cm.
05:30
50.
05:30
50 and 50 to go down by 90 cm.
05:37
So similarly, we can say for 100 cm, like for this much, how much has it gone down?
05:47
So it's gone down, 400 centimeters.
05:51
Same calculation, 90 over 150 into 100, which is basically 900 over 15.
06:00
Or 3, 3505-20.
06:03
60, centimeters.
06:06
So this itself is 60 centimeters.
06:10
this is 60 centimeters.
06:11
And the total was 100 centimeters.
06:14
So that means, this height left over is 40 centimeters.
06:19
Out of that, this height we have to subtract, which was 6.66.
06:24
That means 40 minus 6.66.
06:26
That means somewhere around 33.333 is the minimum length of the mirror.
06:32
Now, remember how I calculated this?
06:34
Basically it depends on the this length, this length, the height of the dog, the height of the person.
06:41
Okay?
06:42
so do you understand?
06:44
Like, was, it clear?
06:45
because this was 60 centimeter in total.
06:48
So that means the leftover is 40 centimeter.
06:51
And this height, what we calculated as, 6.66, that means this leftover.
06:57
let me show that calculation is 40 minus 6.66, which is, 33.33 centimeters.
07:10
Actually, let's take one more question.
07:12
So I, how this can be solved.
07:16
So let's say, the eyes of the person are not always on top, right?
07:19
Let's say the person is 100 centimeter tall.
07:22
And let's say his height, his eyes, is at 20 centimeter below his head.
07:27
Okay?
07:27
So that means this is 80 centimeter.
07:29
Now, let's assume also the distance between.
07:32
okay, sorry.
07:34
Distance between him and the mirror is hundreds.
07:39
So just new to this.
07:40
So bear with me.
07:42
100 centimeters.
07:43
Okay, so if I could ask you, like, what is the minimum length of the mirror for this person to view himself?
07:50
Okay.
07:50
These are his eyes to view himself.
07:54
And the answer, surprisingly, is always the same.
07:57
So let's say the person has a height H.
08:00
The mirror that he required to see yourself fully is H2 always.
08:04
Actually, let's calculate that.
08:06
So that means my answer Simply will be 50 centimeters.
08:10
there is no such shortcut for this question because you'll have to actually calculate it.
08:14
But for this one, let's say it's around the same principle and little simpler.
08:18
So, for his eyes to see his head, the ray will come like this.
08:24
And for his eyes to see his feet, the ray will come like this.
08:28
So that means, See?
08:31
So the ray traveled 100 and 100.
08:33
200 centimeters to go up by 80 centimeters.
08:39
That means how much did it go up in 100 centimeters?
08:42
Half of this, right?
08:44
Or same unitary calculation, 80 by 200.
08:47
Then for 100 it will be 80 by 200 into 100.
08:52
That means divide by two.
08:53
This is 40 centimeters, right?
08:56
Similarly here, the ray went 100.
08:59
100, 200 to go down by 20.
09:02
So 100 to go down by 20.
09:05
So how much?
09:05
Sorry.
09:06
200 to go down by 20.
09:08
So how much to go by 100?
09:09
Half of that.
09:10
That is 10 centimeters.
09:11
So that means, One sec.
09:16
Yeah, but what is 10 cm?
09:19
This much is 10 cm from the head to this point, right?
09:25
It should have been in between.
09:27
So if this is 10 centimeters, this is 40 centimeters.
09:31
That means the mirror that you actually require is just this much.
09:34
Ray, which is not, in this will not form an image.
09:42
But we just require this much.
09:43
A 50 centimeter mirror.
09:45
And we already knew this.
09:46
Since the height is 100 centimeters, our, mirror smallest had to be 50 centimeters.
09:52
So hopefully that gives you, like, a good clarity on what the concept is and all the best for your exam.
Comments
Comments
No comments yet