A double lens system is made of +35.0 cm lens (lens #1) and a -

26.0 cm lens (lens #2).
Lens #1 is placed at x = 0 cm on a meter stick and lens #2 is placed at x = 30.0 cm. Where on the meter stick will the final image be formed when looking at a distant
object?
s2"=f2(f1-d)/f1+f2-d where d=30cm
=6.2cm is that the correct way to do this problem?

To find where the final image will be formed in a double lens system, you can use the lens formula:

1/f1 - 1/f2 = 1/f_total

Here, f1 is the focal length of lens #1, f2 is the focal length of lens #2, and f_total is the combined focal length of the double lens system.

Given that the focal length of lens #1, f1, is +35.0 cm and the focal length of lens #2, f2, is -26.0 cm, we can substitute these values into the lens formula:

1/35 - 1/-26 = 1/f_total

Simplifying the equation, we get:

-26/35 - 35/26 = 1/f_total

Now, we need to solve for f_total:

Multiply both sides of the equation by 35*(-26) to eliminate the denominators:

-26*26 + 35*35 = (35)(-26)(1/f_total)

Simplifying further:

-676 + 1225 = -910/f_total

549 = -910/f_total

To isolate f_total, divide both sides of the equation by 549:

f_total = -910/549

Calculating this expression, we get:

f_total ≈ -1.656 cm

Since the focal length of the double lens system is negative, this indicates that the system acts as a diverging lens. In other words, the image formed will be virtual and will be located on the same side as the object.

Next, we can use the lens formula of a single lens to determine where the final image will be formed. The lens formula is given by:

1/s1' + 1/s2 = 1/f

Here, s1' is the object distance from lens #1, s2 is the image distance from lens #2, and f is the focal length of the double lens system.

Given that s1' = 0 cm (since the object is located at x = 0 cm on the meter stick) and f ≈ -1.656 cm, we can substitute these values into the lens formula:

1/0 + 1/s2 = 1/-1.656

Solving for s2:

1/s2 = 1/-1.656

Invert both sides of the equation:

s2/1 = -1.656/1

s2 ≈ -1.656 cm

The negative sign indicates that the image is formed on the same side as the object, which in this case is at x = 0 cm.

Therefore, the final image will be formed at approximately x = 0 cm on the meter stick when looking at a distant object in this double lens system.

In summary, to solve this problem, we used the lens formula to determine the combined focal length of the double lens system and then applied the lens formula of a single lens to find the image position.