Light is incident at an angle φ with the normal to a plane containing two slits of separation d. Select the expression that correctly describes the positions of the interference maxima in terms of the incoming angle φ and outgoing angle

Question

Light is incident at an angle φ with the normal to a plane containing two slits of separation d. Select the expression that correctly describes the positions of the interference maxima in terms of the incoming angle φ and outgoing angle (A)  sin φ+ sin θ=(m+(1/2)) (λ/d) (B) d sin θ=m λ (C)  sin φ- sin θ=(m+1) (λ/d) (D)  sin φ+ sin θ=m (λ/d)

Tardigrade Admin · Accepted Answer

Path difference =d sin φ+d sin θ For maxima, Δ x=m λ ⇒ sin φ+ sin θ=(m λ/d)

Q. Light is incident at an angle $ϕ$ with the normal to a plane containing two slits of separation $d$ . Select the expression that correctly describes the positions of the interference maxima in terms of the incoming angle $ϕ$ and outgoing angle

$sin ϕ + sin θ = (m + \frac{1}{2}) \frac{λ}{d}$

$d sin θ = mλ$

$sin ϕ - sin θ = (m + 1) \frac{λ}{d}$

$sin ϕ + sin θ = m \frac{λ}{d}$

Path difference $= d sin ϕ + d sin θ$
For maxima, $Δ x = mλ$
$\Rightarrow sin ϕ + sin θ = \frac{mλ}{d}$

Q. Light is incident at an angle ϕ with the normal to a plane containing two slits of separation d. Select the expression that correctly describes the positions of the interference maxima in terms of the incoming angle ϕ and outgoing angle

sinϕ+sinθ=(m+21​)dλ​

dsinθ=mλ

sinϕ−sinθ=(m+1)dλ​

sinϕ+sinθ=mdλ​