Question

In a Young's double slit experiment, $16$ fringes are observed in a certain segment of the screen when light of wavelength $700\text{nm}$ is used. If the wavelength of light is changed to $400\text{nm}$, the number of fringes observed in the same segment of the screen would be

• A. $24$
• B. $30$
• C. $18$
• D. $28$

Answer 1

The correct option is D $28$

Let $n_1$ fringes are visible with light of wavelength ${\lambda }_1\text{and}{n}_2$ with light of wavelength ${\lambda }_2$. Then
$\beta =\frac{n_{1}D{\lambda }_1}{d}=\frac{n_{2}D{\lambda }_2}{d}(\because \beta =\frac{n\lambda D}{d})$
$\Rightarrow \frac{n_2}{n_1}=\frac{{\lambda }_1}{{\lambda }_2}\Rightarrow n_2=\frac{700}{400}\times 16=28$