A single slit diffraction experiment is performed to determine the slit width using the equation, bdD=m , where b is the slit width, D the shortest distance between the slit and the screen, d the distance between the mth diffraction maximum and the central maximum, and is the wavelength. D and d are measured with scales of least count of 1 cm and 1 mm, respectively. The values of and m are known precisely to be 600 nm and 3, respectively. The absolute error (in m) in the value of b estimated using the diffraction maximum that occurs for m=3 with d=5 mm and D=1 m is
Answer
75 to 79
Solution
b= m Dd, so bb= DD+ dd (errors = least counts).
b= 3 600 10-9 15 10-3=3.6 10-4 m=360
bb= 1100+ 15=0.21
b=0.21 360=75.6
(Taking the maximum possible value bmax= 3 600 10-9 1.014 10-3=454.5 gives b 94.5 .)
Answer: 75.6
Official key: [75 to 79] or [94 to 95] accepted.