Visible light of wavelength 6000× 10- 8cm falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at 60o from the central maximum. If the first minimum is produced at θ 1, then θ 1 is close to

Question

Visible light of wavelength 6000× 10- 8cm falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at 60o from the central maximum. If the first minimum is produced at θ 1, then θ 1 is close to (A) 20o (B) 30o (C) 25o (D) 45o

Tardigrade Admin · Accepted Answer

For 2n d minima, dsin θ =2λ sin θ =(√3/2) , (given) ⇒ (λ /d)=(√3/4) ...(1) So, for 1s t minima dsinθ =λ ⇒ sinθ =(λ /d)=(√3/4) ⇒ θ =25.65o ⇒ θ ≈25o

Q. Visible light of wavelength $6000 \times 1 0^{- 8} c m$ falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at $6 0^{o}$ from the central maximum. If the first minimum is produced at $θ_{1},$ then $θ_{1}$ is close to

$2 0^{o}$

$3 0^{o}$

$2 5^{o}$

$4 5^{o}$

For $2^{n d}$ minima,
$d s in θ = 2 λ$
$s in θ = \frac{3}{2}$ , (given)
$\Rightarrow \frac{λ}{d} = \frac{3}{4}$ ...(1)
So, for $1^{s t}$ minima
$d s in θ = λ$
$\Rightarrow s in θ = \frac{λ}{d} = \frac{3}{4}$
$\Rightarrow θ = 25.6 5^{o}$
$\Rightarrow θ \approx 2 5^{o}$

Q. Visible light of wavelength 6000×10−8cm falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at 60o from the central maximum. If the first minimum is produced at θ1​, then θ1​ is close to

20o

30o

25o

45o