Two coherent monochromatic point sources $S_{1}$ and $S_{2}$ of wavelength $λ = 600 n m$ are placed symmetrically on either side of the center of the circle as shown. The sources are separated by a distance d = 1.8 mm. This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is $Δ θ$ . Which of the following options is/are correct?

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

A dark spot will be formed at the point $P_{2}$

At $P_{2}$ the order of the fringe will be maximum

The angular separation between two consecutive bright spots decreases as we move from $P_{1}$ and $P_{2}$ along the first quadrant

The total number of bright fringes produced between $P_{1}$ and $P_{2}$ in the first quadrant is close to 3000

answer is A, C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Question Image

A) at point $P_{1}$ path difference $Δ x = 0$ (central maxima) at point $P_{2}$ path difference $Δ x = d$
Question Image
$n = \frac{Δ x}{λ} = \frac{1.8 \times 10^{- 3}}{600 \times 10^{- 9}}$
$n = 3000$ (maxima)
C) As the path difference is maximum at $P_{2}$ the order of the fringe will be maximum.
D) Angular fringe width increases as we more from $P_{1}$ and $P_{2}$ as shown below
path difference = $x = d \sin θ$
$∴ Δ x = d \cos θ . Δ θ ∴ λ = d \cos θ . Δ θ$
$Δ θ = \frac{λ}{d \cos θ}$ as $θ$ increases $\cos θ$ decreases and $Δ θ$ increases.

Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET