Question

In a Biprism experiment, if the wavelength of red light used is 6.5 $\times {10}^{-7}$ m and that of green is 5.2 $\times {10}^{-7}$ m, the value of n for which (n+1)th green bright band coincides with the $n^{th}$ red bright band for the same setting is given by-

• A. 2
• B. 3
• C. 4
• D. 1

Answer 1

The correct option is C 4

$Given:$ $\lambda$ of Red light$=6.5\times {10}^{-7}m$ ; $\lambda$ of green light $=5.2\times {10}^{-7}m$

$Solution:$ We know that, $\beta =\frac{\lambda d}{D}$

given that $n$ fringes of red coinciding with $(n+1)$ green fringes.Then,

$n{\beta }_r=(n+1){\beta }_g$

$\Rightarrow$ $n\times \frac{6.5\times {10}^{-7}d}{D}=(n+1)\times \frac{5.2\times {10}^{-7}d}{D}$

$\Rightarrow$ $n\times 6.5=(n+1)\times 5.2$

$\Rightarrow$ $6.5n=5.2n+5.2$

$\Rightarrow$ $1.3n=5.2$

$\therefore$ $n=4$

$\text{so,the correct option:C}$