Can partial TIR happen? Consider the image present in this link
Here, at point D, TIR happens, but also there is transmission.
Is "total" internal reflection a misnomer?
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Total internal reflection should not be confused with reflection! (Although they are quite the same).
Total internal reflection occurs when the incident light strikes the interface at an angle greater than the critical angle. And the ray should travel from a denser medium to a rarer medium. The light gets totally reflected (All of it is reflected back).
Reflection, on the other hand, is just like light bouncing off a mirror. There is no minimum or maximum angle that is required. The light, in this case, is not guaranteed to be totally reflected. Some of it could simply pass through the interface and be refracted.
At point D, the light is being partially refracted and partially reflected.