Multiple Choice
A camera lens has a focal length of 85mm. At an -number of , what is the aperture diameter of this lens?
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Cameras
Multiple Choice
In many cameras, the sensor is a rectangle with dimensions 15mm × 22mm. You point your camera to take a photo of your friend, who is 1.8m tall. If your camera lens has a 35mm focal length, how far from the camera should your friend stand in order to produce a 22mm-tall image on the sensor?
A
2.90 cm
B
2.86 cm
C
1.13 cm
D
5.92 cm
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Verified step by step guidance1
Identify the given quantities: the object height \(h_o = 1.8\ \text{m}\), the image height on the sensor \(h_i = 22\ \text{mm}\), and the focal length of the lens \(f = 35\ \text{mm}\). Convert all lengths to consistent units, preferably meters or millimeters, for calculation.
Recall the lens formula relating object distance \(d_o\), image distance \(d_i\), and focal length \(f\):
\[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \]
Use the magnification formula which relates the image height and object height to the distances:
\[ M = \frac{h_i}{h_o} = - \frac{d_i}{d_o} \]
From the magnification formula, express \(d_i\) in terms of \(d_o\) and substitute into the lens formula to get an equation with only \(d_o\) as the unknown.
Solve the resulting equation for \(d_o\), which gives the distance your friend should stand from the camera to produce the desired image size on the sensor.
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