a camera's focal length, F, is related to the distance from the subject, S, and the image distanc, I, by the equation 1/S+1/I=1/F

Please show all your steps! thanks you

steps to what?

show all the steps when solving the question !!! pleasee

Sure! I'll explain how to derive the equation and show all the steps involved.

We start with the lens equation, which relates the object distance, the image distance, and the focal length of a lens. The lens equation is given by:

1/f = 1/s + 1/i

Where:
- f is the focal length of the lens
- s is the object distance (distance from the lens to the object)
- i is the image distance (distance from the lens to the image)

Now, let's rearrange the equation to solve for i:

1/f - 1/s = 1/i

Next, let's take the reciprocal of both sides of the equation:

1/(1/f - 1/s) = 1/i

To simplify the left-hand side, we need to find a common denominator for 1/f and 1/s. The common denominator is fs:

(f - s)/(fs) = 1/i

Now, let's take the reciprocal of both sides again:

fs/(f - s) = i

Next, let's multiply both the numerator and the denominator of the left-hand side by f:

(fs * f) / (f - s) = i

Now, we have:

f * s / (f - s) = i

This equation relates the focal length of the lens, the object distance, and the image distance.

However, the given equation in your question is slightly different:

1/s + 1/i = 1/f

To make it match the derived equation, we can multiply the entire equation by (si / f):

(si / f) * (1/s + 1/i) = (si / f) * (1/f)

After simplifying:

(i + s) / f = si / f^2

Now, we can rearrange the equation to solve for i:

i = (fs) / (f - s)

By comparing this equation with the derived equation above, we can see that they are indeed the same. Therefore, the given equation 1/s + 1/i = 1/f is equivalent to the lens equation 1/f = 1/s + 1/i.