Question

A camera has a lens diameter of 0.0444m. What wavelength of light INNANOMETERS must it use to resolvetwo objects 550 m away that are0.00718 m apart?[?] nm

Answer 1

Given:

• Diameter, D = 0.0444 m

,

• Distance, x = 0.00718 m

,

• d = 550 m

Let's find the wavelength in nanometers.

Apply the formula:

$sin\theta=\frac{1.22\lambda}{D}$

Where:

λ is the wavelength,

Also, we have the formula:

$\begin{gathered} sin\theta=\frac{x}{d} \\ \\ sin\theta=\frac{0.00718}{550} \\ \\ sin\theta=1.30545\times10^{-5}\text{ m} \end{gathered}$

Now, plug in 1.30545 x 10⁻⁵ m for sinθ in the first equation.

Where:

D = 0.0444

Thus, we have:

$\begin{gathered} sin\theta=\frac{1.22\lambda}{D} \\ \\ 1.30545\times10^{-5}=\frac{1.22\lambda}{0.0444} \\ \\ \lambda=\frac{1.30545\times10^{-5}*0.0444}{1.22} \\ \\ \lambda=\frac{5.796\times10^{-7}}{1.22} \\ \\ \lambda=4.751\times10^{-7}m \end{gathered}$

In nanometers, the wavelength will be:

$\begin{gathered} \lambda=475.1\times10^{-9}m \\ \\ \lambda=475.1\text{ nm} \end{gathered}$

Therefore, the wavelength in nanometers is 475.1 nm.

• ANSWER:

475.1 nm