Respuesta :
Answer:
24.71 mm
Explanation:
Distance is proportional to focal length, so
d∝f
which means
[tex]\frac{d'_1}{d'_2}=\frac{f_1}{f_2}[/tex]
Magnification of first lens
[tex]M_2=-\frac{d'_1}{d_1}[/tex]
and
[tex]M_2=\frac{h'_1}{h_1}[/tex]
Similarly, magnification of second lens
[tex]M_2=-\frac{d'_2}{d_1}[/tex]
and
[tex]M_2=\frac{h'_2}{h_1}[/tex]
From the above equations we get
[tex]\frac{M_1}{M_2}=\frac{d'_1}{d_2'}[/tex]
and
[tex]\frac{M_1}{M_2}=\frac{h'_1}{h_2'}[/tex]
which means,
[tex]\frac{d'_1}{d_2'}=\frac{h'_1}{h_2'}[/tex]
and
[tex]\frac{d'_1}{d_2'}=\frac{f_1}{f_2}[/tex]
So, we get
[tex]\frac{f_1}{f_2}=\frac{h'_1}{h_2'}\\\Rightarrow f_2=f_1\times\frac{h_2'}{h'_1}\\\Rightarrow f_2=60\times\frac{14}{34}=24.71\ mm[/tex]
∴ Focal length should this camera's lens is 24.71 mm
The digital camera must have a focal length of 24.71 mm, so that the image of the bridge can cover the entire detector.
Given the following data:
Focal length = 60 mm.
Distance 1 = 34 mm.
Distance 2 = 14 mm.
How to determine the focal length for digital camera.
In order to determine the focal length for this digital camera, we would have to derive an expression that relates the distance of the image formed and the focal length.
In Science, the angular magnification of a lens is given by this formula:
[tex]M=\frac{f_o}{f_1}\\\\[/tex]
For the first lens (old):
[tex]M_1=\frac{f_o}{f_1}=\frac{d_o}{d_1}[/tex]
For the second lens (digital):
[tex]M_2=\frac{f_o}{f_2}=\frac{d_o}{d_2}[/tex]
Equating the two equations, we have:
[tex]\frac{M_1}{M_2} =\frac{\frac{f_o}{f_1}=\frac{d_o}{d_1}}{\frac{f_o}{f_2}=\frac{d_o}{d_2}}[/tex]
Simplifying further, we have:
[tex]f_2 = f_1 \times \frac{d_2}{d_1}\\ \\f_2 = 60 \times \frac{14}{34} \\\\f_2 = 60 \times 0.4118[/tex]
Focal length = 24.71 mm.
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