Question

Calculate the wavelength of sodium light In a biprism experiment with sodium light, bands of width 0.0195 cm are observed at 100 cm from slit given On introducing a convex lens 30 cm away from the slit between biprism and screen, two images of the slit are seen 0.7 cm apart at 100 cm distance from the slit.

• A. $\lambda=4450\,\mathring{A}$
• B. $\lambda=5850 \,\mathring{A}$
• C. $\lambda=3650 \,\mathring{A}$
• D. $\lambda=6750\,\mathring{A}$

Answer 1

Answer: (B)

Lens will from image of two sources at $70\, cm$ from lens (i.e. screen)
From magnification of lens a $m=\frac{v}{u}=\frac{h_{i}}{h_{o}}$
$\frac{70}{30}=\frac{0.7 / 2}{d / 2}$
On solving, $d = 0.3 \,cm $
Now, fringes width $\beta =\frac{\lambda D}{d}$
So, $\lambda =\frac{\beta d}{D}=\frac{0.0195 \times 10^{- 2} \times 0.3 \times 10^{- 2}}{1}=5850 \,\mathring{A}$