Question

Screen S is illuminated by two point sources A and B. Another source C sends a parallel beam of light towards the point P on the screen. Line AP is normal to the screen and line AP, BP and CP are in one plane. The distance AP, BP and CP are 3m, 1.5m and 1.5m respectively. The radiant powers of source A and are 90 and 180 W respectively and the beam from C is of the intensity 20 W/m². Calculate the intensity at P on the screen –

• A. 14$\frac{W}{m^{2}}$
• B. 10$\frac{W}{m^{2}}$
• C. 10$\frac{m^{2}}{W}$
• D. 14$\frac{m^{2}}{W}$

Answer 1

Answer: (A)

14$\frac{W}{m^{2}}$

Answer 2

As A and B are point sources,

\ I =$\frac{L\cos\theta}{r^{2}}$=$\frac{\varphi\cos\theta}{4\pi r^{2}}$ (as f = 4pL)

\ I_A =$\frac{90\cos 0º}{4\pi \times (3)^{2}}$=$\frac{10}{4\pi}\frac{W}{m^{2}}$; I_B =$\frac{180\cos 60º}{4\pi(1.5)^{2}}$=$\frac{10}{\pi}\frac{W}{m^{2}}$

As source C gives a parallel beam of light,

I_C = I₀ cos q = 20 × cos 60º = 10$\frac{W}{m^{2}}$

I = I_A + I_B + I_C =$\frac{10}{4\pi}$+$\frac{10}{\pi}$+ 10 = 10$\left\lbrack \frac{5 + 4\pi}{4\pi} \right\rbrack$ $\simeq$14$\frac{W}{m^{2}}$

Therefore the answer is (1).