question_answer

An electric lamp is fixed at the ceiling of a circular tunnel as shown is figure. What is the ratio the intensities of light at base A and a point B on the wall

A)            1 : 2

B)            \[2:\sqrt{3}\]

C)            \[\sqrt{3}:1\]

D)            \[1:\sqrt{2}\]

Correct Answer: D

Solution :

                   \[{{I}_{A}}=\frac{L}{{{(2r)}^{2}}}\] and \[{{I}_{B}}=\frac{L}{{{\left( r\sqrt{2} \right)}^{2}}}\cos \theta \]               \[=\frac{L}{2{{r}^{2}}}.\frac{r}{r\sqrt{2}}\]\[=\frac{L}{2\sqrt{2}\ {{r}^{2}}}\]            \[\therefore \frac{{{I}_{A}}}{{{I}_{B}}}=\frac{2\sqrt{2}}{4}=\frac{1}{\sqrt{2}}\]