Question 291: Wave Optics

Question

In biprism experiment, if $5^{	ext {th }}$ bright band with wavelength $\lambda_1$ coincides with $6^{	ext {th }}$ dark band with wavelength $\lambda_2$ then the ratio $\left(\lambda_1 / \lambda_2ight)$ is

Accepted Answer

In the biprism experiment, if the 5th bright band with wavelength $\lambda_1$ coincides with the 6th dark band with wavelength $\lambda_2$, we can find the ratio $\frac{\lambda_1}{\lambda_2}$ using the following equations:
Given that the position of the 5th bright band for $\lambda_1$ is the same as the position of the 6th dark band for $\lambda_2$:
$ y_5 = y_6' $
The position of the bright band is given by:
$ \left(\frac{n \lambda D}{d}\right)_5 = \left[\frac{(2n-1) \lambda D}{2d}\right]_6 $
Substituting the values for the 5th bright band and 6th dark band:
$ \frac{5 \lambda_1 D}{d} = \frac{11 \lambda_2 D}{2d} $
By solving this equation, we find:
$ \frac{\lambda_1}{\lambda_2} = \frac{11}{10} $

Answer

$\frac{7}{9}$

Answer

$\frac{10}{11}$

Answer

$\frac{11}{10}$

Answer

$\frac{9}{7}$

Wave Optics

In biprism experiment, if 5^{\text {th }} bright band with wavelength \lambda_1 coincides with 6^{\text {th }} dark band with wavelength \lambda_2 then the ratio \left(\lambda_1 / \lambda_2\right) is

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