Final answer:
The new time taken to prepare a similar print when the distance is increased to 40 cm is 12.8 seconds, calculated using the inverse square law of light intensity.
Step-by-step explanation:
The subject of this question falls under the domain of Physics, which often involves calculations related to light and energy. When a point light source is moved from 25 cm to 40 cm away from the sheet, the intensity of the light on the sheet and therefore the energy received per unit area decreases. According to the inverse square law of light, the intensity of light is inversely proportional to the square of the distance from the source. Therefore, if the distance is increased, the time taken to expose the print properly will also increase.
If the initial distance (d1) is 25 cm and the new distance (d2) is 40 cm, the ratio of the squares of the distances is (d2/d1)^2. So, the new time taken (t2) can be calculated using the ratio of the squares of the distances because the time required is directly proportional to the inverse of the light intensity. This gives us t2 = t1 * (d2/d1)^2 = 5s * (40/25)^2 = 5s * (1.6)^2 = 5s * 2.56 = 12.8 seconds.