Question

a diffraction-limited laser of length l and the laser beam diameter 0.50 cm generates light of wavelength 700 nm. if the beam is directed at the surface and the radius of the illuminated area on the surface is approximately 45 cm, how far away is the surface?
○ 1.1 km
○ 2.2 km
○ 1.3 km
○ 2.6 km
○ 3.2 km

Explanation:

Step1: Recall the diffraction formula for the radius of the illuminated area

The formula for the radius \( r \) of the illuminated area due to diffraction is \( r = \frac{1.22 \lambda D}{d} \), where \( \lambda \) is the wavelength of light, \( D \) is the distance from the laser to the surface (what we need to find), and \( d \) is the diameter of the laser beam. We can rearrange this formula to solve for \( D \): \( D=\frac{r d}{1.22 \lambda} \).

Step2: Convert all units to meters

• The radius \( r = 45 \, \text{cm} = 0.45 \, \text{m} \)
• The diameter \( d = 0.50 \, \text{cm} = 0.0050 \, \text{m} \)
• The wavelength \( \lambda = 700 \, \text{nm} = 700 \times 10^{-9} \, \text{m}=7\times 10^{-7} \, \text{m} \)

Step3: Substitute the values into the formula

Substitute \( r = 0.45 \, \text{m} \), \( d = 0.0050 \, \text{m} \), and \( \lambda = 7\times 10^{-7} \, \text{m} \) into the formula for \( D \):

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Answer:

2.6 km