Question

Irina finds an unlabeled box of fine needles and wants to determine how thick they are. A standard ruler will not do the job, as each needle is less than a millimeter thick. So, to find the thickness, she uses a needle to poke a hole in a piece of brown construction paper. Then, she positions a 640 nm laser pointer to shine through the hole and project a circular diffraction pattern on a wall 23.2 m away. She then uses her ruler to measure that the central bright circle is 16.7 cm in diameter. What diameter does Irina calculate for the needle?

Answer 1

central bright spot is 23.2 cm in dia

the first dark spot ( minima) in diffraction has occurred at y= 8.35 cm

screen distance D = 23.2 m

taking small angle approximation

p = sin(p) = Tan (p) = 8.35e-2/23.2 = 0.36e-2 rad

for diffraction

a sin(p) = ( m=1 , first order)

a = 640e-9/ 0.36e-2 = 1.8 e-4 m

= 0.18 mm