Question

A single slit diffraction is obtained using a beam of red light. If red light is replaced by blue light, what happens?

• A. The diffraction pattern disappears
• B. There is no change in the diffraction pattern
• C. Diffraction fringes becomes narrower and crowded together
• D. Diffraction fringes become broader and farther apart

Answer 1

The correct option is C Diffraction fringes becomes narrower and crowded together

For red light $\lambda ={\lambda }_r$
$\therefore {\beta }_{red}=\frac{D}{a}{\lambda }_r-----\left(i\right)$
For blue light, $\lambda ={\lambda }_b$
$\therefore {\beta }_{blue}=\frac{D}{a}{\lambda }_b------\left(ii\right)$
$\therefore \frac{{\beta }_{blue}}{{\beta }_{red}}=\frac{\frac{D}{a}{\lambda }_b}{\frac{D}{a}{\lambda }_r}=\frac{{\lambda }_b}{{\lambda }_r}\Rightarrow {\beta }_{blue}=\frac{{\lambda }_b}{{\lambda }_r}\times {\beta }_{red}\therefore {\lambda }_b<{\lambda }_r\therefore {\beta }_{blue}<{\beta }_{red}$
$\therefore$ Diffraction fringes become narrower and crowed together.