00:01
So we start with the thin lens formula, 1 over do plus 1 over the i is equal to 1 over f.
00:11
So we are told that the object is 18 centimeters from the lens and we do not know where the image is formed.
00:18
However, we do know that the focal length is 12 and since it's a diverging lens, therefore the focal length will be negative.
00:26
So we can now say 1 over di is equal to negative 1.
00:32
Over 12 minus 1 over 18 and that gives you di is equal to negative 7 .2 centimeters.
00:42
So from here we can find the magnification which is negative di over do so negative of negative 7 .2 divided by 18 and that gives 0 .4.
00:57
Now the question says that we want to reduce the size of the image by a factor of 2, which means that our desired magnification, let's call that m prime, is equal to 0 .4 divided by 2, which is 0 .2.
01:19
So the magnification that we are looking for is 0 .2.
01:23
And therefore, magnification is, which is negative, d .i.
01:28
Over d .o.
01:30
That means we can say that d .i...