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Difficulty: EasyWave Phenomena: Reflection, Refraction, Interference, Diffraction, and Polarization

A monochromatic beam of light with a wavelength of 600 nm600\text{ nm} in air enters a glass block of refractive index 1.501.50. What is the wavelength of the light inside the glass block in nanometers (nm\text{nm})?

Answer: 400 nm

Answer

The wavelength of the light inside the glass block is 400 nm400\text{ nm}.
The speed and wavelength of light both decrease by a factor of the refractive index nn when entering a medium from air, while the frequency stays constant (v=fλv = f\lambda). Thus, λ=λ0n=6001.50=400 nm\lambda = \frac{\lambda_0}{n} = \frac{600}{1.50} = 400\text{ nm}.

Step-by-Step Solution

1
Identify the relevant formula connecting refractive index and wavelength
λ=λ0n\lambda = \frac{\lambda_0}{n}
When light passes from air into a medium, its frequency remains unchanged while its speed and wavelength decrease proportionally by a factor of the refractive index nn.
2
Substitute the given values into the equation
λ=600 nm1.50\lambda = \frac{600\text{ nm}}{1.50}
The wavelength in air is 600 nm600\text{ nm} and the refractive index of glass is 1.501.50.
3
Perform the calculation
λ=400 nm\lambda = 400\text{ nm}
Dividing 600600 by 1.501.50 yields 400400.

Key Concept

Refraction and Wavelength Change in a Medium
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Topics

Wave Phenomena: Reflection, Refraction, Interference, Diffraction, and Polarization

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