Final answer:
By doubling the thickness of the sample, the transmitted intensity of light will be reduced to 25% of the original intensity, as Beer-Lambert's Law dictates that absorbance is directly proportional to the path length.
Step-by-step explanation:
The student's question pertains to the concept of Beer-Lambert's Law in optics, a part of Physics. When the thickness of a sample solution is doubled, assuming all other factors remain constant, the transmitted intensity of light through the solution is expected to decrease further.
According to Beer-Lambert's Law, absorbance (A) is directly proportional to the path length (l), which in this case is equivalent to the thickness of the sample. The relationship can be expressed as A = εlc, where ε is the molar absorptivity, l is the path length, and c is the concentration of the solution.
Since the intensity of light emerging from the sample is 50% of the incident intensity, it suggests that the absorbance is such that it allows half the light to pass through.
If the thickness is doubled, the path length (l) also doubles, which would increase the absorbance. According to the exponential decay relationship I = I0e-A, where I is the transmitted intensity, I0 is the original intensity, and A is the absorbance, a doubling in absorbance due to the increase in thickness would result in a transmitted intensity that is a square of the fraction of the original intensity transmitted (0.52 = 0.25 or 25%). Thus, the transmitted intensity would become 25% of the original intensity after doubling the path length.