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?
One more step:
6.2cm+30cm=36.2cm
To determine where the final image will be formed using the formula s2 = f2(f1 - d)/f1 + f2 - d, where d is the distance between the lenses, f1 is the focal length of lens #1, and f2 is the focal length of lens #2, let's calculate it step by step.
Given:
f1 = +35.0 cm
f2 = -26.0 cm (negative sign indicates a diverging lens)
d = 30.0 cm (distance between the lenses)
To calculate the position of the final image, we can substitute the values into the formula:
s2 = f2(f1 - d)/f1 + f2 - d
Substituting the values:
s2 = (-26.0 cm)[(+35.0 cm) - (30.0 cm)] / (+35.0 cm) + (-26.0 cm) - (30.0 cm)
Simplifying:
s2 = (-26.0 cm)(5.0 cm) / (+9.0 cm) - (30.0 cm)
s2 = -130.0 cm cm / (-21.0 cm)
s2 ≈ 6.19 cm
So the final image will be formed approximately 6.19 cm from lens #2, which is the lens placed at x = 30.0 cm on the meter stick. Therefore, your answer of 6.2 cm is correct.