The minimum possible diameter of the spot on the wall, also known as the diffraction-limited spot size, can be calculated using the formula:
θ = 1.22 λ/D
where θ is the angular size of the spot, λ is the wavelength of the laser, and D is the diameter of the circular opening.
In this case, the wavelength of the laser is 4.00 × 10^14 Hz, which corresponds to a vacuum wavelength of approximately 750 nm (assuming a speed of light of 3.00 × 10^8 m/s). We convert the diameter of the circular opening to meters: 4 mm = 0.004 m.
Substituting these values into the formula, we get:
θ = 1.22 × (750 nm) / (0.004 m) = 0.229 radians
To find the diameter of the spot on the wall, we can use the formula:
d = 2 r = 2 (L tan θ)
where d is the diameter of the spot on the wall, r is the radius of the spot, and L is the distance from the circular opening to the wall.
Substituting the values we know, we get:
d = 2 (9 m tan 0.229) = 0.003 m
So the minimum possible diameter of the spot on the wall is approximately 3 mm (rounded to two significant figures).