Question

The distance between two consecutive bright bands in a bi-prism experiment is 0.32 mm When the red light of wavelength 6400 A is used. by how much will this distance change if the light is substituted by the blue light of wavelength 4800 A with the same setting?

Answer 1

Given that,

Wave length of red light ${\lambda }_r=6400\stackrel{\circ }{A}$

Wave length of blue light ${\lambda }_b=4800\stackrel{\circ }{A}$

Fringe width for red light $X_r=0.32mm$

Fringe width $X=\frac{\lambda D}{d}$

Now, for red light

$X_r=\frac{{\lambda }_{r}D}{d}....\left(I\right)$

For blue light

$X_b=\frac{{\lambda }_{b}D}{d}....\left(II\right)$

Now, dividing equation (II) by(I)

$\frac{X_b}{X_r}=\frac{{\lambda }_b}{{\lambda }_r}$

$X_b=\frac{{\lambda }_b}{{\lambda }_r}\times X_r$

$X_b=\frac{4800}{6400}\times 0.32$

$X_b=0.24mm$

Now, the change in fringe width

$\Delta X=X_r-X_b$

$\Delta X=0.32-0.24$

$\Delta X=0.08mm$

Hence, the change in fringe width is $0.08mm$