Question

The angular separation of the central maximum in the Fraunhofer diffraction pattern is measured. The slit is illuminated by the light of wavelength $6000\, \mathring{A}$. If the slit is illuminated by light of another wavelength, the angular separation decrease by $30 \%$. The wavelength of light used is

• A. $6000\, \mathring{A}$
• B. $3500\, \mathring{A}$
• C. $4200 \, \mathring{A}$
• D. $4700 \, \mathring{A}$

Answer 1

Answer: (C)

Given, wavelength of used light, $\lambda_1=6000 \mathring{A}$
Initial angular separation, $\beta_1=\beta$
Final angular separation, $\beta_2=\beta-30 \%$ of $\beta$
$\beta_2=\beta-0.3 \beta=0.7 \beta$
We know that, $\beta \propto \lambda$
$ l l \Rightarrow \frac{\beta_1}{\beta_2}=\frac{\lambda_1}{\lambda_2} $
$\Rightarrow \lambda_2=\frac{\beta_2 \times \lambda_1}{\beta_1}=\frac{0.7 \beta \times 6000}{\beta}=4200 \mathring{A}$