In Young's double slit experiment the slits are 0.5 mm apart and the interference is observed on a screen at a distance of 100 cm from the slit. It is found that the 9 text th bright fringe is at a distance of 7.5 mm from the second dark fringe from the centre of the fringe pattern on same side. Find the wavelength of the light used.

Question

In Young's double slit experiment the slits are 0.5 mm apart and the interference is observed on a screen at a distance of 100 cm from the slit. It is found that the 9 text th bright fringe is at a distance of 7.5 mm from the second dark fringe from the centre of the fringe pattern on same side. Find the wavelength of the light used. (A) 5000 mathringA (B) 3000 mathringA (C) 7000 mathringA (D) None

Tardigrade Admin · Accepted Answer

(9 D λ/ d )-(3/2) ( D λ/ d ) =7.5 mm , d =0.5 × 10-6 ( D λ/ d )[9-1.5] =7.5 mm , d =5 × 10-7 ( D λ/ d )=1 mm (1 × λ/0.5 × 10-3)=1 × 10-3 ⇒ λ=5000 mathringA

$5000 \overset{˚}{A}$

$3000 \overset{˚}{A}$

$7000 \overset{˚}{A}$

None

$\frac{9 D λ}{d} - \frac{3}{2} \frac{D λ}{d}$
$= 7.5 mm, d = 0.5 \times 1 0^{- 6}$
$\frac{D λ}{d} [9 - 1.5]$
$= 7.5 mm, d = 5 \times 1 0^{- 7}$
$\frac{D λ}{d} = 1 mm$
$\frac{1 \times λ}{0.5 \times 1 0 ^{- 3}} = 1 \times 1 0^{- 3}$
$\Rightarrow λ = 5000 \overset{˚}{A}$

5000A˚

3000A˚

7000A˚

None

d9Dλ​−23​dDλ​ =7.5mm,d=0.5×10−6 dDλ​[9−1.5] =7.5mm,d=5×10−7 dDλ​=1mm 0.5×10−31×λ​=1×10−3 ⇒λ=5000A˚

$5000 \overset{˚}{A}$

$3000 \overset{˚}{A}$

$7000 \overset{˚}{A}$

$\frac{9 D λ}{d} - \frac{3}{2} \frac{D λ}{d}$
$= 7.5 mm, d = 0.5 \times 1 0^{- 6}$
$\frac{D λ}{d} [9 - 1.5]$
$= 7.5 mm, d = 5 \times 1 0^{- 7}$
$\frac{D λ}{d} = 1 mm$
$\frac{1 \times λ}{0.5 \times 1 0 ^{- 3}} = 1 \times 1 0^{- 3}$
$\Rightarrow λ = 5000 \overset{˚}{A}$