SATHEE: Optics 7 Question 45

Optics 7 Question 45

46. Screen $S$ is illuminated by two point sources $A$ and $B$ . Another source $C$ sends a parallel beam of light towards point $P$ on the screen (see figure). Line $A P$ is normal to the screen and the lines $A P, B P$ and $C P$ are in one plane. The distances $A P, B P$ and $C P$ are in one plane. The radiant powers of sources $A$ and $B$ are $90 W$ and $180 W$ respectively. The beam from $C$ is of intensity $20 W / m^{2}$ . Calculate intensity at $P$ on the screen.

$(1982, 5 M)$

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Answer:

Correct Answer: 46. (a) $15 c m$ (b) $1.16 c m$ (downwards) reflection of light

Solution:

Resultant intensity at $P$

$\begin{aligned} I_{P} & = I_{A} + I_{B} + I_{C} \\ = \frac{P_{A}}{4 π (P A)^{2}} + \frac{P_{B}}{4 π (P B)^{2}} \cos 60^{\circ} + I_{C} \cos 60^{\circ} \\ = \frac{90}{4 π (3)^{2}} + \frac{180}{4 π (1.5)^{2}} \cos 60^{\circ} + 20 \cos 60^{\circ} \\ = 0.79 + 3.18 + 10 = 13.97 W / m^{2} \end{aligned}$

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Optics 7 Question 45

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