In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by 5 × 10-2 m towards the slits, the change in fringe width is 3 × 10-3 cm. If the distance between the slits is 1 mm, then the wavelength of the light will be nm .

Question

In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by 5 × 10-2 m towards the slits, the change in fringe width is 3 × 10-3 cm. If the distance between the slits is 1 mm, then the wavelength of the light will be nm . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

β=(λ D / d ) Δ β=(λ/ d ) Δ D λ=(Δ β . d /Δ D ) =(3 × 10-5 × 1 × 10-3/5 × 10-2) =60 × 10-8=600 × 10-9 m =600 nm

β=dλD​ Δβ=dλ​ΔD λ=ΔDΔβ.d​ =5×10−23×10−5×1×10−3​ =60×10−8=600×10−9m =600nm

$β = \frac{λ D}{d}$
$Δ β = \frac{λ}{d} Δ D$
$λ = \frac{Δ β . d}{Δ D}$
$= \frac{3 \times 1 0 ^{- 5} \times 1 \times 1 0 ^{- 3}}{5 \times 1 0 ^{- 2}}$
$= 60 \times 1 0^{- 8} = 600 \times 1 0^{- 9} m$
$= 600 nm$