Question

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

• A.

  $28$

• B. $24$
• C. $30$
• D. $18$

Answer 1

The correct option is A

$28$

Step 1: Given;

$$\begin{gathered} n_1=16 \\ {\lambda }_1=400nm \\ {\lambda }_2=700nm \end{gathered}$$

Step 2: Formula used;

Fringe width, $y=n\frac{D\lambda }{d}$

where, $n=$the number of fringes

$D=$distance between the slit and the screen

$d=$width of the slit

Step 3: Find the number of fringes, $n_2$ when the wavelength is ${\lambda }_2=400nm$

$$\begin{gathered} n_1\frac{D{\lambda }_1}{d}=n_2\frac{D{\lambda }_2}{d} \\ \Rightarrow \frac{n_1}{n_2}=\frac{{\lambda }_2}{{\lambda }_1} \\ \Rightarrow n_2=n_1\frac{{\lambda }_2}{{\lambda }_1} \\ \Rightarrow n_2=16\times \frac{700}{400}=28 \end{gathered}$$

Thus, option A is correct.