Optics: Find & Confirm Image Positions w/ Ray Diagrams

[questions_uk]

Thanks.

 

[questions_uk]

Hi there. Just a quick question regarding an equation. In order to find the transverse magnification of an object 10 mm high and 5 mm long, it gives the equation:

fo / xo = xi / fi = - yi / yo giving xo x xi / fo x fi

Now which part of that is supposed to be used to calculate the transverse magnification?

Am not sure why some variables are equated to other variables e.g. xo x xi = fo x fi

Thanks.

 

[Doc Al]

Hi there. Just a quick question regarding an equation. In order to find the transverse magnification of an object 10 mm high and 5 mm long, it gives the equation:

fo / xo = xi / fi = - yi / yo giving xo x xi / fo x fi

Now which part of that is supposed to be used to calculate the transverse magnification?

Am not sure why some variables are equated to other variables e.g. xo x xi = fo x fi

The definition of transverse magnification is:
m ≡ yi/yo

It can be shown (using similar triangles) that:
m ≡ yi/yo = -si/so (Where si is the image distance; so is the object distance. Both measured from the lens.)

If you measure distances from the focal points (xi & xo are the image and object distances measured from the focal points), then you can show (using the thin lens equation) that:
xi * xo = f*f

m ≡ yi/yo = -xi/f = -f/xo

Using that last term is the easy way to calculate the transverse magnification.

 

[questions_uk]

Thanks.