Speed of light in a medium with refractive index n is which of the following?

Speed of light in a medium with refractive index n is which of the following?

• A. v = c / n
• B. v = c
• C. v = n c
• D. v = c √n

Answer: (A)

Light slows down in a medium by exactly the factor given by the refractive index. By definition, n = c / v, where c is the speed of light in vacuum and v is the speed in the medium. Rearranging gives v = c / n. Since n is typically greater than 1, the light’s speed in the medium is less than in vacuum. The frequency stays the same across the boundary, while the wavelength shortens to λ = λ0 / n. The other expressions would imply no slowing, or speeds faster than c, which contradicts how refractive index governs light’s propagation in media.

Light slows down in a medium by exactly the factor given by the refractive index. By definition, n = c / v, where c is the speed of light in vacuum and v is the speed in the medium. Rearranging gives v = c / n. Since n is typically greater than 1, the light’s speed in the medium is less than in vacuum. The frequency stays the same across the boundary, while the wavelength shortens to λ = λ0 / n. The other expressions would imply no slowing, or speeds faster than c, which contradicts how refractive index governs light’s propagation in media.