Question

In a biprism experiment, the micrometer readings for the zero order and ${10}^{th}$ order fringe are $1.25mm$ and $2.37mm$ respectively, when light of $600nm$ is used. If the wavelength is changed to $750nm$, What will be the respective position of zero and ${10}^{th}$ order fringes ?

• A. $1.25mm,2.65mm$
• B. $1.52mm,2.56mm$
• C. $1.26mm,2.28mm$
• D. $1.32mm,2.65mm$

Answer 1

Answer: (A)

$1.25mm,2.65mm$

Since the reading of micrometer for zero order is non-zero, there is a zero error equal to 1.25mm

Hence this needs to be subtracted to find the true positions of fringes.

Distance between zero order and ${10}^{th}$ order=$2.37mm-1.25mm=1.12mm$.

Now since position of n${}^{th}$ order fringe is $y_n=\frac{nD\lambda }{d}$,

$\frac{\Delta y_n}{y_n}=\frac{\Delta \lambda }{\lambda }=\frac{150}{600}=0.25$

Therefore new $y_n^{\prime }=y_n+\Delta y_n=1.25y_n=1.25\times 1.12mm=1.4mm$

Adding the zero error of the micrometer gives the new position of 10${}^{th}$ fringe at $2.65mm$

Obviously the position of the zero order fringe remains unchanged.