A two-slit Young's interference experiment is done with monochromatic light of wavelength 6000 overset° A . These slits are 2 mm apart. The fringes are observed on a screen placed 10 cm away from the slits. A transparent plate of thickness of 0.5 mm is placed in front of one of the slits. It is found that the interference pattern shifts by 5 mm . What is the refractive index of the transparent plate?

Question

A two-slit Young's interference experiment is done with monochromatic light of wavelength 6000 overset° A . These slits are 2 mm apart. The fringes are observed on a screen placed 10 cm away from the slits. A transparent plate of thickness of 0.5 mm is placed in front of one of the slits. It is found that the interference pattern shifts by 5 mm . What is the refractive index of the transparent plate? (A) 1.2 (B) 1.5 (C) 1.8 (D) 4/3

Tardigrade Admin · Accepted Answer

textShift = (μ - 1) ( texttD/ textd) 5 × 1 0- 3 = (μ - 1) × (( text0.5) × 1 0- 3 × 1 0 × 1 0- 2/2 × 1 0- 3) â (μ - 1) = (1/5) â μ = (6/5) = text1.2

$1.2$

$1.5$

$1.8$

$4/3$

$Shift = (μ - 1) \frac{tD}{d}$
$5 \times 1 0^{- 3} = (μ - 1) \times \frac{( 0.5 ) \times 1 0 ^{- 3} \times 10 \times 1 0 ^{- 2}}{2 \times 1 0 ^{- 3}}$
$\Rightarrow (μ - 1) = \frac{1}{5}$
$\Rightarrow μ = \frac{6}{5} = 1.2$

1.2

1.5

1.8

4/3

Shift=(μ−1)dtD​ 5×10−3=(μ−1)×2×10−3(0.5)×10−3×10×10−2​ ⇒(μ−1)=51​ ⇒μ=56​=1.2

$1.2$

$1.5$

$1.8$

$4/3$

$Shift = (μ - 1) \frac{tD}{d}$
$5 \times 1 0^{- 3} = (μ - 1) \times \frac{( 0.5 ) \times 1 0 ^{- 3} \times 10 \times 1 0 ^{- 2}}{2 \times 1 0 ^{- 3}}$
$\Rightarrow (μ - 1) = \frac{1}{5}$
$\Rightarrow μ = \frac{6}{5} = 1.2$