Physics

Problem

A single slit diffraction experiment is performed to determine the slit width using the equation,

\frac{bd}{D} = m\lambda

, where

b

is the slit width,

D

the shortest distance between the slit and the screen,

d

the distance between the

m^{\text{th}}

diffraction maximum and the central maximum, and

\lambda

is the wavelength.

D

and

d

are measured with scales of least count of 1 cm and 1 mm, respectively. The values of

\lambda

and

m

are known precisely to be 600 nm and 3, respectively. The absolute error (in

\mu\text{m}

) in the value of

b

estimated using the diffraction maximum that occurs for

m = 3

with

d = 5 \text{ mm}

and

D = 1 \text{ m}

is _____.