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) $15 cm$ (b) $1.16 cm$ (downwards) reflection of light
Solution:
- Resultant intensity at $P$
$$ \begin{aligned} I _P & =I _A+I _B+I _C \\ & =\frac{P _A}{4 \pi(P A)^{2}}+\frac{P _B}{4 \pi(P B)^{2}} \cos 60^{\circ}+I _C \cos 60^{\circ} \\ & =\frac{90}{4 \pi(3)^{2}}+\frac{180}{4 \pi(1.5)^{2}} \cos 60^{\circ}+20 \cos 60^{\circ} \\ & =0.79+3.18+10=13.97 W / m^{2} \end{aligned} $$
