Question

A photographic plate placed a distance of 5 cm from a weak point source is exposed for 3 s. If the plate is kept at a distance of 10 cm from the source, the time needed for the same exposure is _____________ .

Options

• 3s

• 12s

• 24s

• 48s

Answer 1

12s

 

Here,

\[d_1  = 5  cm = 0 . 05  m\]

\[ d_2  = 10  cm   =   0 . 1  m\]

\[ t_1  = 3  s\]

\[ t_2  = ?\]

Let the actual incident illuminance be \[E_o\]

Let the iluminance at 3cm distance be \[E_{d1}\]

Let the iluminance at 10cm distance be \[E_{d2} \]

\[\cos\theta   =   1\]

\[ E_{d1}  = \frac{E_o}{{d_1}^2}\]

Now,

\[   t_1   \alpha\frac{1}{E_{d1}}\]

\[ \Rightarrow    t_1    = \frac{k}{E_{d1}}\]

\[ \Rightarrow  t_1  = \frac{k 5^2}{E_o}\]

\[ \Rightarrow \frac{k}{E_o} = \frac{3}{25}\]

Similarly,

\[ \Rightarrow  t_2  = \frac{k {10}^2}{E_o}\]

\[ \Rightarrow  t_2  = \frac{3}{25} \times  {10}^2  = 12  s\]