Published by:
CGP EDU Academic Team
Published on: September 13, 2026
A monochromatic beam of light of wavelength 6000 Å in vacuum enters a medium of refractive index 1.5. In the medium its wavelength is .........., its frequency is .........
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Calculate the wavelength in the medium using the formula:
\( \lambda' = \frac{\lambda}{n} \)
where \( \lambda = 6000 \: \text{Å} = 6000 \times 10^{-10} \: \text{m} \) and \( n = 1.5 \).
\( \lambda' = \frac{6000 \times 10^{-10}}{1.5} = 4000 \times 10^{-10} \: \text{m} = 4000 \: \text{Å} \)
Step 2: The frequency of light remains constant when it enters a medium. Thus, to find the frequency, use the formula:
\( f = \frac{c}{\lambda} \), where \( c = 3 \times 10^8 \: \text{m/s} \).
First, calculate the frequency in vacuum:
\( f = \frac{3 \times 10^8}{6000 \times 10^{-10}} = 5 \times 10^{14} \: \text{Hz} \).
Therefore, the answers are: wavelength in medium = 4000 Å, frequency = 5 x 10^14 Hz.
\( \lambda' = \frac{\lambda}{n} \)
where \( \lambda = 6000 \: \text{Å} = 6000 \times 10^{-10} \: \text{m} \) and \( n = 1.5 \).
\( \lambda' = \frac{6000 \times 10^{-10}}{1.5} = 4000 \times 10^{-10} \: \text{m} = 4000 \: \text{Å} \)
Step 2: The frequency of light remains constant when it enters a medium. Thus, to find the frequency, use the formula:
\( f = \frac{c}{\lambda} \), where \( c = 3 \times 10^8 \: \text{m/s} \).
First, calculate the frequency in vacuum:
\( f = \frac{3 \times 10^8}{6000 \times 10^{-10}} = 5 \times 10^{14} \: \text{Hz} \).
Therefore, the answers are: wavelength in medium = 4000 Å, frequency = 5 x 10^14 Hz.
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