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, $\beta \propto \lambda$
$ll\Rightarrow \frac{{\beta }_1}{{\beta }_2}=\frac{{\lambda }_1}{{\lambda }_2}$
$\Rightarrow {\lambda }_2=\frac{{\beta }_2\times {\lambda }_1}{{\beta }_1}=\frac{0.7\beta \times 6000}{\beta }=4200\mathring{A}$