SATHEE: Optics Question 501

Optics Question 501

Question: A lamp is hanging along the axis of a circular table of radius r. At what height should the lamp be placed above the table, so that the illuminance at the edge of the table is $\frac{1}{8}$ of that at its center

[MP PET 2005]

Options:

A) $\frac{r}{2}$

B) $\frac{r}{\sqrt{2}}$

C) $\frac{r}{3}$

D) $\frac{r}{\sqrt{3}}$

Show Answer

Answer:

Correct Answer: D

Solution:

$\frac{I_{c e n t e r}}{I_{e d g e}} = \frac{{(r^{2} + h^{2})}^{3 / 2}}{h^{3}}$

$\Rightarrow 8 = \frac{{(r^{2} + h^{2})}^{3 / 2}}{h^{3}}$

$\Rightarrow 2 h = {(r^{2} + h^{2})}^{1 / 2}$

$\Rightarrow 4 h^{2} = r^{2} + h^{2}$

$\Rightarrow 3 h^{2} = r^{2}$

Therefore $h = \frac{r}{\sqrt{3}}$

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Optics Question 501

Question: A lamp is hanging along the axis of a circular table of radius r. At what height should the lamp be placed above the table, so that the illuminance at the edge of the table is 18 of that at its center

Options:

Answer:

Solution:

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Question: A lamp is hanging along the axis of a circular table of radius r. At what height should the lamp be placed above the table, so that the illuminance at the edge of the table is $\frac{1}{8}$ of that at its center