Optics 6 Question 20

22. In the adjacent diagram, CP represents a wavefront and AO and BP, the corresponding two rays. Find the condition of θ for constructive interference at P between the ray BP and reflected ray OP

(2003,2M)

(a) cosθ=3λ2d

(b) cosθ=λ4d

(c) secθcosθ=λd

(d) secθcosθ=4λd

Show Answer

Solution:

  1. PR=d

PO=dsecθ and CO=POcos2θ=dsecθcos2θ

path difference between the two rays is,

Δx=PO+OC=(dsecθ+dsecθcos2θ)

phase difference between the two rays is Δφ=π (one is reflected, while another is direct)

Therefore, condition for constructive interference should be

Δx=λ2,3λ2

or

dsecθ(1+cos2θ)=λ2

or

dcosθ(2cos2θ)=λ2 or cosθ=λ4d



जेईई के लिए मॉक टेस्ट

एनसीईआरटी अध्याय वीडियो समाधान

दोहरा फलक