Questions: d = (1 × 2.97 m × 635 nm) / (0.007 m) =

Solution Steps

We are given the following values in the problem:

• \(1\) (a dimensionless constant)
• \(2.97 \, \text{m}\) (a length in meters)
• \(635 \, \text{nm}\) (a wavelength in nanometers)
• \(0.007 \, \text{m}\) (a length in meters)

Convert the wavelength from nanometers to meters: \[ 635 \, \text{nm} = 635 \times 10^{-9} \, \text{m} \]

Substitute the given values into the formula: \[ d = \frac{1 \times 2.97 \, \text{m} \times 635 \times 10^{-9} \, \text{m}}{0.007 \, \text{m}} \]

Calculate the numerator: \[ 2.97 \times 635 \times 10^{-9} = 1.88595 \times 10^{-6} \, \text{m}^2 \]

Now, divide by the denominator: \[ d = \frac{1.88595 \times 10^{-6} \, \text{m}^2}{0.007 \, \text{m}} = 2.6942 \times 10^{-4} \, \text{m} \]

Final Answer