Question

The optimum diameter d (in millimeters) of the pinhole in a pinhole camera can be modeled by d=1.9[(5.5×10−4)L]1/2, where is the length (in millimeters) of the camera box. Find the optimum pinhole diameter for a camera box with a length of 10 centimeters. Round your answer to the nearest hundredth.

Answer 1

The optimum pinhole diameter for a camera box with a length of 10 centimeters is 0.446 mm

Solution:

Given that,

The optimum diameter d (in millimeters) of the pinhole in a pinhole camera can be modeled by:

$d = 1.9[(5.5 \times 10^{-4})l]^{\frac{1}{2}}$

where l is the length (in millimeters) of the camera box

Find the optimum pinhole diameter for a camera box with a length of 10 centimeters

l = 10 cm

We know that,

10 cm = 100 mm

Therefore, plug in l = 100 in given formula

$d = 1.9[(5.5 \times 10^{-4}) \times 100]^{\frac{1}{2}}\\\\d = 1.9[5.5 \times 10^{-4} \times 10^2]^{\frac{1}{2}}\\\\d = 1.9[5.5 \times 10^{-2}]^{\frac{1}{2}}\\\\d = 1.9 \times 5.5^{\frac{1}{2} \times 10^{-1}}\\\\d = 0.19 \times 2.345207\\\\d = 0.4455 \approx 0.446$

Thus the optimum pinhole diameter for a camera box with a length of 10 centimeters is 0.446 mm