First slide

Coherent sources and their importance in interference

Question

A source emits electromagnetic waves of wavelength 3 m. One beam reaches the observer directly and other after reflection from a water surface, travelling 1.5 m extra distance and with intensity reduced to 1/4 as compared to intensity due to the direct beam alone. The resultant intensity will be

Moderate

A

(1/4) fold
B

(3/4) fold
C

(5/4) fold
D

(9/4) fold

Solution

$W e k n o w t h a t a p h a s e c h a n g e o f π o c c u r s w h e n t h e r e f l e c t i o n t a k e p l a c e a t t h e b o u n d a r y o f d e n s e r m e d i u m . D u e t o g e o m e t r y, ∆ ϕ_{1} = \frac{2 π}{λ} ∆ x = \frac{2 π}{3} (1.5) = π r a d i a n . D u e t o p h a s e c h a n g e, ∆ ϕ_{2} = π r a d i a n ∴ T o t a l p h a s e d i f f e r e n c e o f s e c o n d w a v e w h e n i t r e a c h e d t h e o b s e r v e r ∆ ϕ = ∆ ϕ_{1} + ∆ ϕ_{2} = 2 π r a d i a n R e s u l \tan t i n t e n s i t y = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos ϕ = I + \frac{I}{4} + 2. \frac{I}{2} \cos (2 π) = \frac{5 I}{4} + I = \frac{9 I}{4}$

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