Questions: A student is getting her picture taken by a digital camera. The student is h0=1.55 m tall and she stands d0=4.75 m in front of the camera lens which has a focal length of f=0.011 m. what is expression for the resulting image distance, di.

Solution Steps

The lens formula relates the object distance (\(d_0\)), the image distance (\(d_i\)), and the focal length (\(f\)) of a lens. The formula is given by: \[ \frac{1}{f} = \frac{1}{d_0} + \frac{1}{d_i} \]

We are given the following values:

• Object distance, \(d_0 = 4.75 \, \text{m}\)
• Focal length, \(f = 0.011 \, \text{m}\)

Substitute these values into the lens formula: \[ \frac{1}{0.011} = \frac{1}{4.75} + \frac{1}{d_i} \]

First, calculate \(\frac{1}{0.011}\) and \(\frac{1}{4.75}\): \[ \frac{1}{0.011} \approx 90.9091 \] \[ \frac{1}{4.75} \approx 0.2105 \]

Now, substitute these values back into the equation: \[ 90.9091 = 0.2105 + \frac{1}{d_i} \]

Isolate \(\frac{1}{d_i}\): \[ \frac{1}{d_i} = 90.9091 - 0.2105 \approx 90.6986 \]

Finally, solve for \(d_i\): \[ d_i = \frac{1}{90.6986} \approx 0.0110 \, \text{m} \]

Final Answer