Suppose you wanted to be able to see astronauts on the moon. What is the smallest diameter of the objective lens required to resolve a 0.60 m object on the moon? Assme the wavelength of the light is near the middle of the visible spectrum: 550 nm yellow light.
A: 4.25×10^2 B: 4.97×10^2 C: 5.82×10^2 D: 6.81×10^2 E: 7.96×10^2 F: 9.32×10^2 G: 1.09×10^3 H: 1.28×10^3
=> θ1 = 1.22λ/D
=> w = (2.44*λ *L)/D
w is width; L is length from screen to object.
The Attempt at a Solution
So I know we are calculating the diameter of the lens needed so I solved the equation for D and got:
w = (2.33*λ *L)/D
after this step I converted all my values to meters and got: these values:
(2.44*5.5E-7m*3.97E8m) / 0.6m = 888.6m which is in the range I need but It has to be an exact answer.
Can anyone help me understand what I did wrong?