Explanation 1) Concept: The light intensity at a point on the receiver depends on the difference of path length from the transmitter; the intensity will be maximum at d s i n θ = m λ , when m is an integer, and for minimum intensity d s i n θ = m + 1 2 λ , with m = 0,1 , 2,3 , … But due to phase change of π r a d occurring due to reflection of wave from water, the point of minimum intensity will become point of maximum intensity in this case. 2) Formula: i) sin 2 ⁡ θ = tan 2 ⁡ θ 1 + tan 2 ⁡ θ ii) Binomial theorem 1 ± x 1 2 ≈ 1 ± 1 2 x + … + h i g h e r o r d e r t e r m s 3) Given: i) Lake width, D ii) Height of microwave transmitter from the water level, a iii) Height of receiver from the water level, x iv) Microwave with wavelength λ ≥ a 4) Calculations: Suppose the wave w 1 goes directly to the receiver and covers a distance L 1 and wave w 2 is reflected from water and covers a distance L 2 = L 2 p + L 2 q , and the wave w 2 suffers change of phase of λ 2 . To get constructive interference at the receiver, the difference L 2 - L 1 must be an odd multiple of a λ 2 . Consider the figure given below: D = ( D p + D q ) a In the figure, T a n d R represent transmitter and receiver. D t a n θ = x ( D p + D q ) t a n θ = x t a n θ = x ( D p + D q ) Using formula (i), we get sin ⁡ θ = a + x D 2 + a + x 2 Using the above equation, we will have L 2 p = a s i n θ = a D 2 + a + x 2 a + x And, L 2 q =

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ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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Chapter 35, Problem 89P

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The value of x for which the signal at the receiver R is maximum.

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Chapter 35, Problem 88P

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Chapter 35 Solutions

Fundamentals of Physics Extended

Ch. 35 - Does the spacing between fringes in a two-slit...Ch. 35 - a If you move from one bright fringe in a two-slit...Ch. 35 - Figure 35-22 shows two light rays that are...Ch. 35 - In Fig. 35-23, three pulses of lighta, b, and cof...Ch. 35 - Is there an interference maximum, a minimum, an...Ch. 35 - Figure 35-24a gives intensity I verus position x...Ch. 35 - Figure 35-25 shows two sources S1 and S2 that emit...Ch. 35 - Figure 35-26 shows two rays of light, of...Ch. 35 - Light travels along the length of a 1500-nm-long...Ch. 35 - Figure 35-27a shows the cross section of a...

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To find The value of x for which the signal at the receiver R is maximum.

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To find The value of x for which the signal at the receiver R is maximum.

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Chapter 35 Solutions

To find

The value of x for which the signal at the receiver R is maximum.