Question

A lamp is hanging at a height of 40cm from the centre of the table. If height of lamp is increased by 10cm, illuminance of the table will
A) increase by 10%
B) decreases by 10%
C) increases by 36%
D) decreases by 36%

Answer 1

The illuminance on the table will depend on the distance of the light source placed as, the illuminance is inversely proportional to the square of the distance at which the light source is placed. Also, this is valid only if the light source is the same for first and the second case.

Formula used:
$I=\dfrac{L}{{{r}^{2}}}$

Complete step by step answer:
Let us write down the given values,
The height at which the lamp is placed initially is 40cm.
The final height is equal to 50cm.
Now, the illuminance of the light source depends on the distance eat which it is placed as,
$I=\dfrac{L}{{{r}^{2}}}$
Initially, the illuminance of the lamp will be,
${{I}_{1}}=\dfrac{L}{1600}$
Finally,
The illuminance of the lamp after the source is moved by some distance will be,
${{I}_{2}}=\dfrac{L}{2500}$ the change in the illuminance of the light source or the lamp will be equal to,
$\begin{aligned} & \%I=(\dfrac{{{I}_{2}}-{{I}_{1}}}{{{I}_{2}}})\times 100 \\\ & \therefore \%I=\dfrac{900}{2500}\times 100=36\% \\\ \end{aligned}$
Therefore, the correct option is option d.

Additional information:
The illuminance of the light source is inversely proportional to the distance at which the light source is placed. It is because as the light source is moving away from the light source and the area that must be covered by the light is more. Thus, the number of particles hitting a point of the area decreases, which means the intensity of the light decreases. Also, the l in the above formula is the intensity of the light projected. As the light lamp is the same in both the cases, the l is taken constant. If it is different, the illuminance will change accordingly.

Note:
The terms luminance and illuminance are a lot different. Illuminance is the amount of light falling onto a given surface area. Luminance is the amount of light passing through the object. The amount of light that hits the street below is illuminance. We can measure the illuminance using an illuminance meter.