In Young's double-slit experiment, the slits are 2mm apart and are illuminated with a mixture of two wavelength λ 1=750nm and λ 2=900nm . The minimum distance from the common central bright fringe on a screen 2m from the slits where a bright fringe from one interference pattern coincides with a bright fringe from the other is:

Question

In Young's double-slit experiment, the slits are 2mm apart and are illuminated with a mixture of two wavelength λ 1=750nm and λ 2=900nm . The minimum distance from the common central bright fringe on a screen 2m from the slits where a bright fringe from one interference pattern coincides with a bright fringe from the other is: (A) 1.5mm (B) 3mm (C) 4.5mm (D) 6mm

Tardigrade Admin · Accepted Answer

n1λ 1=n2λ 2 n1× 750× 10- 9=n2× 900× 10- 9 (n1/n2)=(6/5)n1=6,n2=5 x1=(n1 D λ 1/ d) x1=(6 × 2 × 750 × 10- 9/2 × 10- 3) x1=4.5mm

$1.5 mm$

$3 mm$

$4.5 mm$

$6 mm$

$n_{1} λ_{1} = n_{2} λ_{2}$
$n_{1} \times 750 \times 1 0^{- 9} = n_{2} \times 900 \times 1 0^{- 9}$
$\frac{n _{1}}{n _{2}} = \frac{6}{5} n_{1} = 6, n_{2} = 5$
$x_{1} = \frac{n _{1} D λ _{1}}{d}$
$x_{1} = \frac{6 \times 2 \times 750 \times 1 0 ^{- 9}}{2 \times 1 0 ^{- 3}}$
$x_{1} = 4.5 mm$

1.5mm

3mm

4.5mm

6mm

n1​λ1​=n2​λ2​ n1​×750×10−9=n2​×900×10−9 n2​n1​​=56​n1​=6,n2​=5 x1​=dn1​Dλ1​​ x1​=2×10−36×2×750×10−9​ x1​=4.5mm

$1.5 mm$

$3 mm$

$4.5 mm$

$6 mm$

$n_{1} λ_{1} = n_{2} λ_{2}$
$n_{1} \times 750 \times 1 0^{- 9} = n_{2} \times 900 \times 1 0^{- 9}$
$\frac{n _{1}}{n _{2}} = \frac{6}{5} n_{1} = 6, n_{2} = 5$
$x_{1} = \frac{n _{1} D λ _{1}}{d}$
$x_{1} = \frac{6 \times 2 \times 750 \times 1 0 ^{- 9}}{2 \times 1 0 ^{- 3}}$
$x_{1} = 4.5 mm$