JEE Main & Advanced
Physics
Ray Optics
Question Bank
Photometry
question_answer
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]
A) 1 : 1
B) 2 : 1
C) \[2\sqrt{2}:1\]
D) 3 : 2
Correct Answer:
C
Solution :
Illuminance at A, \[{{I}_{A}}=\frac{L}{{{h}^{2}}}\] Illuminance at B, \[{{I}_{B}}=\frac{L}{\sqrt{{{({{h}^{2}}+{{r}^{2}})}^{2}}}}\cos \theta \] \[=\frac{Lh}{{{({{r}^{2}}+{{h}^{2}})}^{3/2}}}\] \[\therefore \frac{{{I}_{A}}}{{{I}_{B}}}={{\left( 1+\frac{{{r}^{2}}}{{{h}^{2}}} \right)}^{3/2}}\]\[={{\left( 1+\frac{{{8}^{2}}}{{{8}^{2}}} \right)}^{3/2}}={{2}^{3/2}}=2\sqrt{2}:1\]