If the distance between the first maxima and fifth minima of a double slit pattern is $7 \mathrm{~mm}$ and the slits are separated by $0.15 \mathrm{~mm}$ with the screen 50 $\mathrm{cm} .$ from the slits, then the wavelength of the light used is:

• A

  $200 \mathrm{nm}$
• B

  $100 \mathrm{nm}$
• C

  $800 \mathrm{nm}$
• Correct answer
  D

  $600 \mathrm{nm}$

Solution

There are three and a half fringes from first maxima to fifth minima as shown.
$\Rightarrow \beta=\frac{7 \mathrm{~mm}}{3.5}=2 \mathrm{~mm} \Rightarrow \lambda=\frac{\beta \mathrm{D}}{\mathrm{d}}=600 \mathrm{nm}$

Hence, the correct answer is option: 'D'.