Question

A photographic plate is placed directly in front of a small diffused source in the shape of a circular disc. It takes 12s to get a good exposure. If the source is rotated by 60° about one of its diameter, the time needed to get the same exposure will be ___________ .

Options

• 6s

• 12s

• 24s

• 48s

Answer 1

24s

 

Here,

\[ t_1  = 12  s\]

\[ \theta_1  =  0^0 \]

\[ \theta_2  =  {60}^0 \]

\[ t_2  = ?\]

Let the distance be r.

Let the incident luminosity be \[E_o.\]

We have,

\[ E_\theta1  = \frac{E_o {\cos\theta}_1}{r^2}\]

\[ t_1 \alpha  \frac{1}{E_\theta1}\]

\[ \Rightarrow  t_1  = \frac{r^2 k}{E_o {\cos\theta}_1}\]

\[ \Rightarrow 12 = \frac{r^2 k}{E_o \cos0}\]

\[ \Rightarrow \frac{r^2 k}{E_o} = 12\]

Similarly,

\[ t_2  = \frac{r^2 k}{E_o {\cos\theta}_2} = \frac{12}{\cos( {60}^0 )}\]

\[ \Rightarrow  t_2  = 12 \times 2 = 24  s\]