00:01
Okay, so in this question, we are to repeat the previous question, but for the case of a convex mirror.
00:10
So let's go ahead and get down the givens.
00:12
We're told that the height is 0 .6 centimeters.
00:17
And so i'm going to go ahead and actually call that y, because that's the notation that your book is using.
00:23
So y is equal to 0 .6 centimeters.
00:30
And the object position is 16 .5, and it's positive because it's to the left of the mirror, and so that's 16 .5 centimeters.
00:41
And the radius of curvature of the mirror is 22 centimeters.
00:50
And since it's convex, i'm going to call this radius negative.
00:56
And so we want to first draw a principal ray diagram and calculate the position.
01:01
Size orientation and then the nature of the image.
01:06
And so i'm going to actually perform the calculation first.
01:09
So to find the image information about the image, we want to use the formula 1 over s plus 1 over s prime equals 2 over r.
01:26
And so if we solve this for 1 over s prime, we can do that by bringing the 1 over s to the other side.
01:33
And so we got that it's equal to 2 over r minus 1 over s.
01:46
And then therefore, if you invert both sides, then you get the s prime is equal to all of this raised to the negative first power.
01:59
So if i go ahead and plug in the numbers here, let's see what i get.
02:07
I'm going to go to my calculator on desmos.
02:12
Whoops, not a four function.
02:15
And, oops.
02:20
So that's 1 over 11, negative 1 over 11 minus 1 divided by 16 .5.
02:29
And with that, i obtain that the image is, oh, take that to the minus first power.
02:37
And with that, i obtain the image is at a position of negative 6 .6.
02:41
So i can say therefore that s prime is equal to negative six.
02:48
Whoops.
02:57
Great.
02:58
And so that means that it's on the right side of the mirror because it's a virtual image.
03:06
So from the negative, we know it's virtual.
03:13
And to find out if it's inverted, we want to look at its magnification.
03:18
So the magnification is minus s.
03:24
Is it s prime over s? let me just double check real quick.
03:28
I'm not sure why i'm blanking on it.
03:30
Yeah, s prime.
03:31
S prime over s.
03:38
Yeah, i guess that makes sense.
03:40
So then that's 6 .6 divided by 16 .5.
03:46
And the important thing, though, is that it's positive.
03:51
So that means it's upright.
04:00
And what other information did they want? position size.
04:05
Oh yeah, let's go ahead and get the size.
04:07
So if the magnification is this, then the size of the image is 6 .6 divided by 16 .5 times the size of the original image, which is 0 .6.
04:22
These are some kind of ugly numbers if i have to say so.
04:26
So let me go ahead and calculate that.
04:28
So 6 .6 divided by 16 .5, multiplied by 0 .6.
04:36
And then i get that the image is 0 .24 centimeters.
04:45
Okay, so it's going to be a little smaller and should be upright, and hopefully i return that in my diagram.
04:55
So i'm going to go ahead and draw my diagram on the next page.
05:03
So let's try to do it accurately.
05:06
Of challenging with these but i'm going to try to take advantage of using the whole screen.
05:12
But yeah, i want to try to actually use the lines instead of drawing my own.
05:19
Oops.
05:23
So here's my line.
05:29
Oops, what happened to that? give me one second, maybe, maybe multiple seconds.
05:48
Okay, i have to use the delete button.
05:51
It's kind of hard to track this across.
05:56
Okay, that's pretty good.
05:59
Oh, where did it go? i'm not sure if i should keep trying or give up let me just undo that.
06:12
Okay, the undo worked and i think for now.
06:16
I'm just gonna give up so go back to just drawing it.
06:28
Great, and so we know that the r is 22, so f is at about 11.
06:35
So let's draw our our f here...