Question

A parallel beam of light of wavelength $500\, nm$ falls on a narrow slit and the resulting diffraction pattern is observed on a screen $1 \,m$ away. It is observed that the first minima is at a distance of $2.5\, mm$ from the centre of the screen. The width of the slit is

• A. $0.2 \,mm$
• B. $1 \,mm$
• C. $2 \,mm$
• D. $1.5 \,mm$

Answer 1

Answer: (A)

$0.2 \,mm$

Answer 2

Width of slit, $d = \frac{n\lambda D}{x}$ Here, $n = 1, D = 1 m$, $x = 2.5\, mm = 2.5 \times 10^{-3} m$ $\lambda = 500\, nm = 500\times 10^{-9}m$ $\therefore d = \frac{1\times 500\times 10^{-9}\times 1}{2.5\times 10^{-3}}$ $=2 \times 10^{-4} m = 0.2 \,mm$