Question

In Fresnel biprism experiment, when light of wavelength $6000A^o$ is used then $16th$ bright fringes is obtained at point $P$. If light of wavelength $4800A^o$ is used then the order of the fringe obtained at point $P$ will be

• A. ${16}^{th}$
• B. ${20}^{th}$
• C. ${18}^{th}$
• D. ${24}^{th}$

Answer 1

The correct option is B ${20}^{th}$

In a fresnel bi-prism, fringe width $\beta =\frac{\lambda D}{d}$

$\beta =\frac{6000\times D}{d}$

distance of P from central line (=position of 16th fringe)$=16\beta ;$
now, new fringe width $\beta \prime =\frac{4800\times D}{d}$
$\therefore$ order of fringe at P now $=\frac{16\beta }{\beta \prime }=\frac{\left(\frac{16\times 6000\times D}{d}\right)}{\left(\frac{4800\times D}{d}\right)}=20$