Optical components - lens and mirror

AI Thread Summary
The discussion focuses on solving problems related to optical components, specifically diverging lenses and mirrors. For part (a), the calculations for the object distance and image position using magnification formulas are presented, with a proposed object distance of 3f and an image distance of -0.5f. In part (b), the user questions the applicability of certain formulas for determining the image position after reflection from the mirror, indicating uncertainty about their approach. Part (c) involves finding the distance d for a fourfold reduction in image size, resulting in a calculated distance of 5f and an image position of -3.75f. The user seeks validation and advice on their solutions.
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Homework Statement


a) Despite the diverging lens with focal length f we observed object which is perpendicular to the optical axis (Figure 6 in the article ,,5. Rozptylka a zrcátko"). To what distance from the diverging lens we have to put the subject to be scaled twice? (cross-magnification Z = 1 / 2). Determine also the position of the image of subject.

b) NextLOK to the diverging lens we placed a mirror perpendicular to the optical axis of the distance d from the lens. The rays pass through the lens, reflected from the mirror and then again pass through the lens. Where we will find the image of object and what will be its cross-magnification?

c) How we have to choose a distance d that the resulting image will be four times smaller than the object? Where we will see the final image?

1. The attempt at a solution
a) I use this equations:
Z = -a'/a = -(a'-f/f) = -(f/(a-f) = 1/2 (minus only for decisions - the image upright / inverted)
a = f(Z+1)/Z = f*1,5/0,5 = 3f
a' = f(Z-1) = f*(0,5-1) = -0,5f
Is right?

b) Ok, I can draw it, but numerically... Hehe.
Can I use the typical formula Z=y'/y = - a'/a = -(a'-f)/f = -f/(a-f) ? I think NO, but I try it.
Z = -f/(d-f); a' = Z*d = -fd*(d-f)

c)
Hmmm... Also the formula.
Z = -f/(a-f)
d=f(Z+1)/Z = f*(0,25+1)/0,25=5f
a, = -Z*d = -0,25*5f = -3,75f

Ok, this is my solutions. What do you think about it? What is true, what is false? Please, give me a advice, thank you.
 
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