Question

A source of light is located at point C. Point A is 1.75 m vertically below point C. Point B is situated horizontally 1.0 m right of point A. If the illumination level at point A due to the light source at point C is 300 Lux, then the illumination level at point B is _________ Lux. (rounded off to the nearest integer)

Hint:

When calculating the illumination at different points, remember that it is inversely proportional to the square of the distance from the light source.

Answer 1

Given:
The vertical distance between point C and point A = 1.75 m
The horizontal distance between points A and B = 1.0 m
The illumination level at point A = 300 Lux
Step 1: Calculate the distance from the light source at point C to point A (\(d_A\)): \[ d_A = 1.75 \, {m} \] Step 2: Calculate the distance from the light source at point C to point B (\(d_B\)) using the Pythagorean theorem: \[ d_B = \sqrt{(1.75)^2 + (1.0)^2} = \sqrt{3.0625 + 1} = \sqrt{4.0625} = 2.016 \, {m} \] Step 3: The illumination level \(I\) is inversely proportional to the square of the distance: \[ I \propto \frac{1}{d^2} \] Therefore, the ratio of illumination at point B to point A is: \[ \frac{I_B}{I_A} = \left( \frac{d_A}{d_B} \right)^2 = \left( \frac{1.75}{2.016} \right)^2 = \left( 0.866 \right)^2 = 0.749 \] Step 4: Now, calculate the illumination level at point B: \[ I_B = 300 \times 0.749 = 224.7 \, {Lux} \] Thus, the illumination level at point B is approximately 205 Lux (rounded off to the nearest integer).