Question

A slit of width a is illuminated by white light. The first minimum for red light $(\lambda =6500\stackrel{0}{A})$ will fall at $\theta =30$ when a will be:

• A. 3200 $\stackrel{0}{A}$
• B. $6.5\times {10}^{-4}mm$
• C. 1.3 micron
• D. $2.6\times {10}^{-4}cm$

Answer 1

The correct option is C 1.3 micron

Given: The wavelength of the red light is $6500A^o$.

The angle at which the light falls is ${30}^{\circ }$.

To find: The width of the slit.

Path difference between the beams of the light is:

$\Delta x=n\lambda$

For first minimum, $n=1$

$\Delta x=a\times sin\theta =1\lambda$

$a=\frac{\lambda }{sin\theta }=\frac{6.5\times {10}^{-7}}{sin{30}^o}$

$=13\times {10}^{-7}=1.3micron$