Physics, asked by shahidmahar3827, 1 year ago

A newton's ring arrangement is used with a source emitting two wavelengths a1 = 6 x 10 cm and 4.5 x 10 cm and it is found that the nh dark ring due to 1 coincides with (n + 1)th dark ring for 12. If the radius of curvature of the curved surface is 60 cm, find the diameter of nth dark ring

Answers

Answered by csh57875
1

Answer:

Given: λ₁= 6 x 10 cm

λ₂=4.5 x 10 cm

R=60 cm

(D n )λ₁=(D n+1 )λ₂

Formula:

(D n ²) =4nλ

Solution:

for nth dark ring λ₁,

(D n ²) λ1=4nλ₁  ....(1)

for (n+1)th dark ring λ₂,

(D n+1 ²) λ1=4(n+1)λ₂   ....(2)

from given ,

(D n )λ₁=(D n+1 )λ₂

squaring on both the sides,

(D n² )λ₁=(D n+1 ²)λ₂

4nλ₁=4(n+1)λ₂ ....( from 1 and 2)

nλ₁=(n+1)λ₂

nλ₁=nλ₂+λ₂

n=λ₂/λ₁-λ₂

n= 4.5x10 /6x 10 - 4.5 x10

n=4.5/1.5

n=3

Using equation 1, the diameter of 3th  dark ring for λ₁ is,

D₃²= 4x3x60x6x10

D₃²=    43200

D₃=207.84 cm (ACCORDING TO GIVEN DATA)

Explanation:

Use concept of radii of newton's dark rings in reflected light.

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