Question

In Young's experiment, the wavelength of red light is $7800\mathring{A}$ and that of blue light is $5200\mathring{A}$. The value of $n$ for which $(n+1)$th blue band coincides with $n$th red band is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

Position of $nth$ red band $y_{red}=\frac{nD{\lambda }_1}{d}$
Position of $(n+)th$ blue band $y_{blue}=\frac{(n+1)D{\lambda }_2}{d}$
For coincidence of bands
or $\frac{nD{\lambda }_1}{d}=\frac{(n+1)D{\lambda }_2}{d}$
or $n{\lambda }_1=(n+1){\lambda }_2$
or $7800n=5200(n+1)$
We get $n=2$