A photographic plate records sufficient intense lines when it is exposed for 12 s to a source of 10 W. How long should it be exposed to a 12 W source radiating the light of same colour to get equally intense lines ?

Answer

To solve the problem, we need to determine how long a photographic plate should be exposed to a 12 W light source to achieve the same energy exposure as when it was exposed to a 10 W light source for 12 seconds.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Power of the first light source (P1) = 10 W
- Time of exposure for the first light source (t1) = 12 s
- Power of the second light source (P2) = 12 W
- Time of exposure for the second light source (t2) = ?

2. **Calculate Energy for the First Source:**
The energy (E1) absorbed by the photographic plate when exposed to the first source can be calculated using the formula:
\[ E_1 = P_1 \times t_1 \]
Substituting the values:
\[ E_1 = 10 \, \text{W} \times 12 \, \text{s} = 120 \, \text{J} \]

3. **Set Up the Equation for the Second Source:**
The energy (E2) absorbed by the photographic plate when exposed to the second source can be expressed as:
\[ E_2 = P_2 \times t_2 \]
Since we want the energies to be equal (E1 = E2), we can write:
\[ E_1 = E_2 \]
Therefore:
\[ 120 \, \text{J} = 12 \, \text{W} \times t_2 \]

4. **Solve for t2:**
Rearranging the equation to find t2:
\[ t_2 = \frac{E_1}{P_2} = \frac{120 \, \text{J}}{12 \, \text{W}} = 10 \, \text{s} \]

5. **Conclusion:**
The time required for the photographic plate to be exposed to the 12 W source to achieve equally intense lines is:
\[ t_2 = 10 \, \text{s} \]

### Final Answer:
The photographic plate should be exposed for **10 seconds** to the 12 W source.