Find the ratio of the size of the image to that of the object

The focal length of a concave lens is 'f''. An object is placed at a distance 'x' from its FIRST FOCAL POINT. The ratio of the size of the image to that of the object is?

That 'ratio of the size of image to that of the object' is the magnification,

using Descartes formula, m = di/do = hi/ho.

So

the object distance is x + f. ( x <-----> f <-------> (mirror) ) hence it's x + f
1/f = 1/do + 1/di
1/f = 1/(x+f) + 1/di
1/di = 1/f - 1/(x+f)
1/di = [(x+f)/f(x+f)] - f/f(x+f)
1/di = [(x+f - f)/f(x+f)]
1/di = x/f(x+f)
di = f(x+f)/x

m = di/do

f(x+f)/x divided by x+f
f(x+f)/x divided by x+f is the same thing as saying multiplied by 1/(x+f)

so f(x+f)/x multiplied by 1/(x+f)

the answer is f/x !

Hope it helps :)

Hi:

the general rule of thumbs is

d1/d2 = Os/Is

d1 = distance of Object
d2= distance of image
Os = object size
Is = Image size

the one use by mathematican ans optical people is

1/s1 + 1/s2 =1 /f

s1 = the distance from the object
s2 = the distance from the image ( or camera distance from the lens of it)
f = the Focal lenght

Here a website to explain it


http://www.physicsclassroom.com/Class/re…

http://www.wilmslowastro.com/software/fo…

http://en.wikipedia.org/wiki/Curved_mirr…

http://en.wikipedia.org/wiki/Focal_lengt…

http://search.yahoo.com/search;_ylt=A0oG…


I hope this helps