A hollow prism is filled with water of refractive index 1.34 and white light is incident on the prism. The white light is assumed to have wavelengths ranging from 4020 Å to 6700 Å. What is the corresponding wavelength range in water?
- A.3000 Å to 5000 Å
- B.4020 Å to 6700 Å
- C.5000 Å to 7000 Å
- D.5386 Å to 8978 Å
Correct answer
Explanation
The correct answer is A, 3000 Å to 5000 Å. When light enters a denser medium, its wavelength is divided by the refractive index of that medium.
The frequency of light is fixed by its source and does not change on refraction. Since speed equals frequency times wavelength, and the speed in water is c/n, the wavelength in water is λ/n. Here 4020 ÷ 1.34 = 3000 Å and 6700 ÷ 1.34 = 5000 Å, so the whole band shrinks to 3000–5000 Å. The colour we see still depends on frequency, so red light in water is still seen as red.
B keeps the wavelengths unchanged, which would be true only if water did not slow light down.
C, 5000 Å to 7000 Å, does not follow from dividing by 1.34 and is close to the air values.
D multiplies the wavelengths by 1.34 instead of dividing, which would make light faster in water than in air.
Exam tip: on refraction, frequency stays the same while speed and wavelength both fall by the factor n.
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