Optics Question 487

Question: A small lamp is hung at a height of 8 feet above the centre of a round table of diameter 16 feet. The ratio of intensities of illumination at the centre and at points on the circumference of the table will be

[CPMT 1984, 1996]

Options:

A) 1 : 1

B) 2 : 1

C) $ 2\sqrt{2}:1 $

D) 3 : 2

Show Answer

Answer:

Correct Answer: C

Solution:

Illuminance at A, $ I _{A}=\frac{L}{h^{2}} $

Illuminance at B, $ I _{B}=\frac{L}{\sqrt{{{(h^{2}+r^{2})}^{2}}}}\cos \theta $

$ =\frac{Lh}{{{(r^{2}+h^{2})}^{3/2}}} $

$ \therefore \frac{I _{A}}{I _{B}}={{( 1+\frac{r^{2}}{h^{2}} )}^{3/2}} $

$ ={{( 1+\frac{8^{2}}{8^{2}} )}^{3/2}}={{2}^{3/2}}=2\sqrt{2}:1 $



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