A 0.1 watt LASER beam with an aperture of 5.0 mm emits light of wavelength 6943 Å.Calculate the areal spread and intensity of the image when the beam is focused with the lenshaving a focal length of 100 mm.

Sure, let's break this down step by step.

1. First, we need to calculate the spread of the beam. The spread of the beam can be calculated using the formula for the diffraction-limited spot size (D) of a lens, which is given by:

   D = 2.44 * λ * f / D0

   where: λ is the wavelength of the light, f is the focal length of the lens, and D0 is the diameter of the beam before it is focused by the lens.

   Substituting the given values into the formula:

   D = 2.44 * (6943 * 10^-10 m) * (100 * 10^-3 m) / (5 * 10^-3 m) D = 3.38 * 10^-4 m or 0.338 mm

2. Next, we need to calculate the areal spread of the image. The areal spread (A) of the image is given by the area of the circle with diameter D, which is given by:

   A = π * (D/2)^2

   Substituting the value of D into the formula:

   A = π * (0.338 * 10^-3 m / 2)^2 A = 8.97 * 10^-8 m^2

3. Finally, we need to calculate the intensity of the image. The intensity (I) of the image is given by the power (P) of the beam divided by the areal spread (A) of the image, which is given by:

   I = P / A

   Substituting the given values into the formula:

   I = 0.1 W / 8.97 * 10^-8 m^2 I = 1.12 * 10^6 W/m^2

So, the areal spread of the image is 8.97 * 10^-8 m^2 and the intensity of the image is 1.12 * 10^6 W/m^2.