ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of incidence 45°. The ray undergoes total internal reflection. If n is the refractive index of the medium with respect to air, select the possible value(s) of n from the following
Question
ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of incidence 45°. The ray undergoes total internal reflection. If n is the refractive index of the medium with respect to air, select the possible value(s) of n from the following
Solution
The phenomenon of total internal reflection occurs when a ray of light travelling from a denser medium (with a higher refractive index) to a rarer medium (with a lower refractive index) hits the boundary at an angle of incidence greater than the so-called critical angle. The critical angle is the angle of incidence for which the angle of refraction is 90 degrees.
The critical angle can be calculated using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media. In the case of total internal reflection, the angle of refraction is 90 degrees, so Snell's law simplifies to:
sin(critical angle) = 1 / n
where n is the refractive index of the denser medium with respect to the rarer medium.
Given that the angle of incidence is 45 degrees and total internal reflection occurs, the critical angle must be less than or equal to 45 degrees. Therefore, we have:
sin(critical angle) <= sin(45 degrees)
which simplifies to:
1 / n <= sin(45 degrees)
or
n >= 1 / sin(45
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