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Question
You are given four sources of light each one providing a light of a single colour – red, blue, green and yellow. Suppose the angle of refraction for a beam of yellow light corresponding to a particular angle of incidence at the interface of two media is 90°. Which of the following statements is correct if the source of yellow light is replaced with that of other lights without changing the angle of incidence?
Options
The beam of red light would undergo total internal reflection.
The beam of red light would bend towards normal while it gets refracted through the second medium.
The beam of blue light would undergo total internal reflection.
The beam of green light would bend away from the normal as it gets refracted through the second medium.
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Solution
The beam of blue light would undergo total internal reflection.
Explanation:
According to the Cauchy relationship, `lambda oo 1/mu`
Smaller the wavelength higher the refractive index and consequently smaller the critical angle.
We know `v = flambda`, the frequency of wave remains unchanged with medium hence `v oo lambda`.
The critical angle, sin C = `1/mu`
Also, velocity of light, `v oo 1/mu`
According to VIBGYOR, among all given sources of light, the blue light have smallest wavelength, As `lambda_("blu") < lambda_("yellow")` hence `v_("blue") < v_("yellow")`, it means `mu_("blue") > mu_("yellow")`
It means critical angle for blue is less than yellow colour, the critical angle is least which facilitates total internal reflection for the beam of blue light.
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