Question

A light wave is incident normally over a single slit of width $24 × 10^{-5}\, cm$. The angular position of second dark fringe from the central maxima is $30^°$. What is the wavelength of light?

• A. $6000\, \mathring{A}$
• B. $5000\, \mathring{A}$
• C. $3000\, \mathring{A}$
• D. $1500\, \mathring{A}$

Answer 1

Answer: (A)

For $n^{th}$ dark fringe in single slit, a $sin\theta = n\lambda$
For second dark fringe, a $sin\theta = 2\lambda$
So, $24 × 10^{-5} × 10^{-2} × sin\, 30^° = 2\lambda$
$\therefore \lambda= 6 × 10^{-7}\, m = 6000\, \mathring{A}$