Thin lens equation for diverging lenses.

[nblu]

Hi, I was reading a section which explains about the
"thin lens equation for diverging lenses" and it included an example;

Formula:
1/f = 1/di + 1/do
where f is the focal distance,
di is the distance of the image from the center and,
do is the distance of the object from the center.

Example:
f = -4cm
do = 3cm
di = ?

1/di = 1/f - 1/do
1/di = -1/4cm - 1/3cm
1/di = -3/12cm - 4/12cm
1/di = -7/12cm
1/di = -12/7cm = -1.7cm

The part where I have a confusion is colored in red.
I've been questioning, why -7/12cm was flipped in the last step.

If that example was to be solved as decimal numbers it would be;
1/di = -0.250cm^-1 - 0.333cm^-1
1/di = -1/0.583cm
then in this case, I would understand why the number has been reversed because it was ^-1
but when solving in fraction, I get confused..

Could anybody please explain for me?
Thank you in advance

 

[Doc Al]

1/di = 1/f - 1/do
1/di = -1/4cm - 1/3cm
1/di = -3/12cm - 4/12cm
1/di = -7/12cm
1/di = -12/7cm = -1.7cm

The part where I have a confusion is colored in red.
I've been questioning, why -7/12cm was flipped in the last step.

I assume it's a typo. That last line should have read:
di = -12/7cm = -1.7cm

I assume that you understand that: 1/x = a/b can be inverted (as long as you're not dividing by zero) to become x = b/a.

 

[ogb p]

Hello,

I can explain the reason for the negative sign and the flipping of the fraction in the last step of the example. The thin lens equation is used to calculate the position of the image formed by a lens. In this equation, the sign of the focal distance (f) is important because it indicates whether the lens is a converging lens (positive f) or a diverging lens (negative f).

In the given example, we are dealing with a diverging lens, which has a negative focal distance of -4cm. When we substitute this value into the equation, it becomes:

1/f = 1/di + 1/do
1/-4cm = 1/di + 1/3cm

As you can see, the negative sign is already included in the value of f. Therefore, when we solve for 1/di, we need to keep the negative sign in the equation. This is why the fraction is flipped in the last step. It is a mathematical rule that when we divide by a negative number, the fraction gets flipped.

To further clarify, let's look at the decimal calculation:

1/di = -0.250cm^-1 - 0.333cm^-1
1/di = -0.583cm^-1
1/di = -1/0.583cm

In this case, we are dealing with the reciprocal of the focal distance, which is -0.583cm^-1. When we convert this to a fraction, we get -1/0.583cm, which is the same as -7/12cm. This is why the fraction is flipped in the last step.

I hope this explanation helps to clear your confusion. If you have any further questions, please feel free to ask. As a scientist, it is my job to help others understand scientific concepts. Thank you.