(a) A 2.40-cm-high insect is 1.30 m from a 135-mm focal-length lens. Where is the image, how high is it, and what type is it? (b) What if f = -135 mm?
a)
f=dFd−F=1.3⋅0.1351.3−0.135=0.15 m,f=\frac{dF}{d-F}=\frac{1.3\cdot 0.135}{1.3-0.135}=0.15~m,f=d−FdF=1.3−0.1351.3⋅0.135=0.15 m,
Γ=fd=0.151.3=0.12.\Gamma=\frac fd=\frac{0.15}{1.3}=0.12.Γ=df=1.30.15=0.12.
Image real, inverted, not magnified.
b)
f=d∣F∣d+∣F∣=1.3⋅0.1351.3+0.135=0.12 m,f=\frac{d|F|}{d+|F|}=\frac{1.3\cdot 0.135}{1.3+0.135}=0.12~m,f=d+∣F∣d∣F∣=1.3+0.1351.3⋅0.135=0.12 m,
Γ=fd=0.121.3=0.09.\Gamma=\frac fd=\frac{0.12}{1.3}=0.09.Γ=df=1.30.12=0.09.
Image virtual, erect, not magnified.
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