question_answer

Two sources of light (\[{{S}_{1}}\] and \[{{S}_{2}}\]) of wave ie r: jib 2500\[\overset{0}{\mathop{A}}\,\] and 3500\[\overset{0}{\mathop{A}}\,\] respectively are used in Youngs double slit experiment simultaneously Find out at which order of two wave trail pattern the fringes coincide.

A)  Fifth order fringe due to \[{{S}_{1}}\] will coincide with seventh order fringe due to \[{{S}_{2}}\]

B)  Fifth order fringe due to \[{{S}_{2}}\]will coincide with seventh order fringe due to

C)  Seventh order fringe due to \[{{S}_{1}}\]             will coincide with sixth order fringe due to \[{{S}_{2}}\]

D)  Seventh order fringe due to \[{{S}_{2}}\] will coincide with sixth order fringe due to \[{{S}_{1}}\]

Correct Answer: B

Solution :

                Let the order of the fringe for\[{{S}_{1}}\]be Up for\[{{S}_{2}}\]be\[{{n}_{2}}\]. Then,        \[{{n}_{1}}{{\lambda }_{1}}={{n}_{2}}{{\lambda }_{2}}\] \[\therefore \]  \[{{n}_{1}}\times 2500={{n}_{2}}\times 3500\] \[\Rightarrow \]               \[\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{35}{25}=\frac{7}{5}\] \[\therefore \]7th order of\[{{S}_{1}}\]will coincide with 5th order of\[{{S}_{2}}\]or 5th order of\[{{S}_{2}}\]will coincide with 7th order of\[{{S}_{2}}\].