The screen of a pinhole camera is at a distance D from the pinhole, which has a diameter d. The light has an effective wavelength λ. (λ ≪ D) For which of the following value of d will the image be sharpest?
A. √(λD)B. λ
C. λ/10
D. λ²/D
E. D²/λ
(GR8677 #100)
Solution: See Pinhole Camera
Order of magnitude:
λ of visible light is 400 to 700 nm or in the order of 10−7 meter.
D is around 10 to 100 cm or in the order of 1 meter.
d is expected to be around 1 mm or in the order of 10−3 meter.
A. TRUE
√(λD) = √(10−7× 1) ≈ 10−3 about the right size of d
B. FALSE
λ → d cannot be in the order of 10−7 meter
C. FALSE
λ/10 → d cannot be in the order of 10−8 meter
D. FALSE
λ²/D ≈ 10−14→ d cannot be too small
E. FALSE
D²/λ ≈ 1/10−7 = 107→ d cannot be too big
Answer: A
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