In a biprism experiment with sodium light, bands of width 0.0195 cm are observed at 100 cm from slit. 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. Calculate the wavelength of sodium light.

Question

In a biprism experiment with sodium light, bands of width 0.0195 cm are observed at 100 cm from slit. 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. Calculate the wavelength of sodium light. (A) λ = text4450 overset° A (B) λ = text5850 overset° A (C) λ = text2650 overset° A (D) λ = text6750 overset° A

Tardigrade Admin · Accepted Answer

Lens will from image of two sources at 70 cm from lens (i.e. screen)
From magnification of lens

m = \frac{v}{u} = \frac{h _{i}}{h _{o}}

\frac{70}{30} = \frac{0.7/2}{d /2}

On solving,

d = 0.3 c m

Now, fringes width

β = \frac{λ D}{d}

So,

λ = \frac{β d}{D} = \frac{0.0195 \times 1 0 ^{- 2} \times 0.3 \times 1 0 ^{- 2}}{1} = 5850 A^{\circ}

$λ = 4450 A^{\circ}$

$λ = 5850 A^{\circ}$

$λ = 2650 A^{\circ}$

$λ = 6750 A^{\circ}$

λ=4450 A∘

λ=5850 A∘

λ=2650 A∘

λ=6750 A∘

Lens will from image of two sources at 70 cm from lens (i.e. screen) From magnification of lens m=uv​=ho​hi​​ 3070​=d/20.7/2​ On solving, d=0.3cm Now, fringes width β=dλD​ So, λ=Dβd​=10.0195×10−2×0.3×10−2​=5850A∘

$λ = 4450 A^{\circ}$

$λ = 5850 A^{\circ}$

$λ = 2650 A^{\circ}$

$λ = 6750 A^{\circ}$